Simultaneous Reversible Data Hiding and Quality Enhancement for VQ-Compressed Images via Quality Improvement Codes

Abstract

With the rapid proliferation of digital multimedia in resource-constrained Internet of Things (IoT) environments, there is growing demand for efficient image compression combined with secure data embedding. Existing Vector Quantization (VQ)-based Reversible Data Hiding (RDH) methods prioritize embedding capacity while neglecting reconstruction fidelity, often introducing noticeable quality degradation in edge regions—unacceptable for high-fidelity applications such as medical imaging and forensic analysis. This paper proposes a lightweight RDH framework with a once-offline trained VQ codebook that simultaneously performs secure data embedding and visual quality enhancement for VQ-compressed images. Quality Improvement Codes (QIC) are generated from pixel-wise residuals between original and VQ-decompressed images and embedded into the VQ index table using a novel Recoding Index Value (RIV) mechanism without additional transmission overhead. Sobel edge detection identifies perceptually sensitive blocks for targeted enhancement. Comprehensive experiments on ten standard test images across multiple resolutions (256 × 256, 512 × 512) and codebook sizes (64–1024) demonstrate Peak Signal-to-Noise Ratio (PSNR) gains of +4 to +5.39 dB and Structural Similarity Index Measure (SSIM) improvements of +4.12% to +9.86%, with embedding capacities approaching 100 Kbits. The proposed approach consistently outperforms existing methods in both image quality and payload capacity while eliminating computational overhead of deep learning models, making it highly suitable for resource-constrained edge devices and real-time multimedia security applications.

1. Introduction

1.1. Background and Motivation

The rapid proliferation of digital multimedia content in modern communication systems has significantly increased the risk of unauthorized copying, manipulation, and distribution of digital images, thereby posing substantial challenges to data security and content integrity [1]. To address these issues, information hiding techniques have emerged as essential tools for imperceptibly embedding confidential information into host media—such as images, audio, or video—for purposes including copyright protection, content authentication, and covert communication [2,3].

Depending on whether the host media can be perfectly restored after data extraction, data hiding techniques are generally classified into irreversible data hiding (IDH) and reversible data hiding (RDH) [4,5]. RDH is particularly valued in mission-critical domains—such as medical imaging, national defense, and forensic analysis—where both the embedded information and the pristine reconstruction of the original carrier are indispensable [6,7].

In practical applications, digital images are often stored or transmitted in compressed formats to satisfy storage and bandwidth constraints. Common compression techniques include Vector Quantization (VQ), Block Truncation Coding (BTC), and Lempel–Ziv–Welch (LZW) [8,9,10]. Consequently, data hiding schemes tailored to compressed images have attracted considerable research attention, with a focus on maintaining high embedding capacity while preserving compression efficiency [1,11,12]. Among these techniques, VQ is a widely adopted block-based lossy compression method that partitions an image into non-overlapping blocks, represents each block as a vector, and encodes it using a codebook generated via clustering algorithms such as Linde–Buzo–Gray (LBG) or its variants [10,11]. VQ offers high compression ratios and low encoding complexity [12], making it suitable for real-time signal processing applications.

Beyond VQ-based RDH, two adjacent research lines are also relevant to our problem setting. First, in content authentication with self-recovery, fragile watermarking schemes have coupled AMBTC-based authentication codes with VQ-based recovery information so that tampered regions can be localized and reconstructed without the original image; such designs explicitly show how VQ indices can serve as an efficient compressed-domain carrier while balancing visual quality and integrity verification [13,14].

VQ-based RDH methods still face persistent and critical challenges that limit their practical deployment. Most existing schemes embed secret data solely within the VQ index table [15], often overlooking the visual quality of the reconstructed image. This quality degradation problem is widespread and severe across multiple scheme categories. For instance, SOC-based methods may introduce file-size expansion alongside quality loss, while JNC-based approaches [16] can result in higher bit rates and visible blocking artifacts. Even reversible schemes, if inadequately designed, introduce noticeable quality degradation that compounds the inherent losses of VQ compression itself.

This quality deterioration is particularly severe in edge regions, where high-frequency details are most vulnerable to quantization errors. Existing schemes can degrade PSNR and introduce visible blocking artifacts, especially near edges [12,17,18], with edge structures exhibiting visible discontinuities and blocking artifacts. Such degradation is unacceptable in high-fidelity applications, including medical imaging (where diagnostic accuracy depends on edge clarity), forensic analysis (where evidence integrity is paramount), and defense communications (where image authenticity must be verifiable). The pervasive nature of this quality-capacity trade-off across existing VQ-based RDH methods underscores the urgent need for approaches that can simultaneously achieve secure embedding and quality enhancement rather than treating them as competing objectives.

Although numerous RDH schemes for VQ-compressed images have been proposed, most existing approaches still suffer from inherent trade-offs between embedding capacity and visual quality. Prior research has primarily focused on LAS-, SOC-, and index-based schemes [12,13], with limited success in addressing quality degradation.

The proliferation of Internet of Things (IoT) devices has intensified the need for efficient multimedia data compression and secure information hiding. Images and videos are now frequently transmitted and processed in diverse application domains, from smart healthcare to industrial monitoring. Recent advances in the Internet of Multimedia Things (IoMT) emphasize the integration of big data analytics to enable smart multimedia applications [19]. In this context, vector quantization (VQ) remains widely adopted due to its simplicity and high compression ratio.

Additionally, learning-based VQ variants have been used to improve reconstruction quality rather than to embed data. For example, a hierarchical VQ-VAE inpainting pipeline trains codebooks on ground-truth images and then leverages multi-dilation refinement to restore corrupted regions with high fidelity, demonstrating that VQ codebooks can encode useful priors for perceptual enhancement [20]. Meanwhile, in digital semantic communication, VQ is used to discretize deep semantic features into indices for channel-adaptive image transmission; recent work further introduces Kullback–Leibler Divergence (KLD)-regularized usage and Exponential Moving Average (EMA)-based updates to mitigate codebook collapse [21]. While these directions emphasize learning-based fidelity or transmission robustness, our framework utilizes pre-trained VQ codebooks without requiring any neural-network training or inference during deployment, thereby enabling the simultaneous enhancement of RDH and image quality in the compressed domain.

Recent advances in VQ-based RDH include difference-index-based schemes, such as those proposed by Li et al. (2020) [4], which enhance embedding capacity through difference transformation and mapping techniques. Chen et al. [22] proposed adaptive prediction-difference coding combined with index rearrangement. Kong et al. [23] introduced adaptive multi-pass embedding based on pixel-value ordering. Gandhi and Kumar [24] presented a comprehensive survey highlighting persistent challenges in balancing capacity, fidelity, and efficiency.

Despite these developments, significant challenges remain, particularly in edge regions where visual distortion is most noticeable. These studies collectively underscore the necessity of developing lightweight approaches that simultaneously enhance reconstruction quality in compressed domains.

Compared with prior approaches such as Chang et al. (2007) [18], Ma et al. (2015) [13], and Li et al. (2020) [4], the present work introduces a new paradigm that leverages pixel-wise residuals between the original and VQ-decompressed images to achieve both reversible data hiding and quality improvement within a unified framework. Unlike learning-based pipelines (e.g., VQ-VAE inpainting and VQ-assisted semantic communication) [20,21], which require large-scale neural-network training and substantial computational resources, the proposed method relies solely on compact IC/DC codebooks trained once offline and requires no neural-network training or inference during deployment, making it lightweight and suitable for low-latency, resource-constrained environments. This design enables practical deployment for secure data embedding while simultaneously enhancing the visual quality of decompressed images.

The rest of this paper is organized as follows: Section 2 presents the proposed materials and methods, including the preprocessing phase, Quality Improvement Code (QIC) generation, and the Recoding Index Value (RIV) mechanism for simultaneous data embedding and quality enhancement. Section 3 reports experimental results and analysis across multiple test images, resolutions, and codebook configurations. Finally, Section 4 provides concluding remarks and outlines directions for future research.

1.2. Related Works

Digital image information hiding techniques aim to imperceptibly embed secret information into carrier media to achieve various objectives, such as content authentication, copyright protection, or secret communication [1,4,10,13]. Based on whether the carrier media can be perfectly restored after secret extraction, information hiding techniques can be divided into two major categories: irreversible data hiding and reversible data hiding (RDH) [7]. The unique feature of RDH technology is that it not only successfully extracts the embedded secret information but also fully restores the original carrier image to its initial state without introducing any distortion. This is critical in many application scenarios with strict requirements for data integrity and distortion-free restoration of the original carrier, such as medical imaging, national defense security, and forensic analysis [4,7], where it is essential to ensure that the original image information can be precisely restored. In recent years, such high-fidelity requirements have also extended to Internet of Things (IoT) applications, particularly in edge-based smart healthcare, industrial monitoring, and surveillance systems, where secure and reversible image processing is essential to ensure traceability and reliability of decision-making.

Data hiding techniques for digital images can be applied across various domains, including the spatial domain, frequency domain, compressed domain, and encryption domain [4,5]. For example, Weng and Yang [25] proposed a multi-hider sharing algorithm for reversible data hiding in encrypted images, highlighting the feasibility of collaborative embedding under encryption scenarios. With the rise of social media and IoT-connected imaging devices (e.g., surveillance cameras, smart drones, and mobile medical sensors), digital images are rapidly generated, transmitted, and compressed to reduce bandwidth consumption and storage cost [3]. Therefore, data hiding in compressed images has become increasingly important for resource-constrained IoT environments, where maintaining low bitrates while preserving image fidelity is crucial [26].

1.2.1. Vector Quantization (VQ)

Vector Quantization (VQ) is a widely used lossy compression method that achieves efficient image representation through block-based coding [8,27]. Its basic principle involves partitioning the original image into non-overlapping pixel blocks, each of which is treated as a multidimensional vector. Before compression, a codebook must be pre-established, containing a set of representative image blocks (i.e., codewords). The codebook is typically trained using the Linde–Buzo–Gray (LBG) algorithm or its improved versions. The LBG algorithm is an iterative algorithm based on k-means clustering, designed to select the most representative codewords from the training images to form the codebook. Using the LBG algorithm, the training images are partitioned into blocks of 4 × 4 pixels each, and then the most representative codewords are selected from these blocks to form a codebook. Each selected codeword is represented as a 16-dimensional vector.

The VQ compression process is as follows: For each block in the image, the algorithm searches the codebook for the most similar codeword (typically measured by calculating the Euclidean distance). The block is then represented by the index value of that codeword. The index values of all blocks collectively form an index table. During decompression, the receiver simply maps each index back to its corresponding codeword using the index table and the pre-shared codebook to reconstruct an image that is approximately identical to the original. VQ is renowned for its high compression ratio and relatively simple encoding and decoding procedures. However, since VQ is a lossy compression technique, the approximation error (i.e., quality loss) of the decompressed image is closely related to the length (or size) of the codebook; the larger the codebook, the smaller the approximation error, and the reconstructed image quality is typically better [4,5].

1.2.2. Data Hiding Techniques for VQ-Compressed Images

Early research on data hiding for VQ-compressed images primarily focused on embedding secret data in the VQ index table and using it as the main carrier. These schemes aimed to increase embedding capacity and reduce bit rates but often failed to adequately consider the quality of the image after VQ decompression. If the hiding scheme is irreversible, or even if it is reversible but improperly implemented, the quality of the VQ-decompressed image may even deteriorate.

The following lists some representative VQ-compressed image data hiding schemes and their main ideas:

• From SOC to Recent Compressed-Domain RDH Directions:

The SOC-based line originates with Chang et al. (2004) [15], which leverages block-wise spatial correlation to more efficiently encode VQ index tables; early SOC-based hiding replaced indicator bits of SOC-coded indices but could expand file size in some cases. Recent work has broadened beyond SOC in three representative ways: (a) VQ codebook–level reversible embedding that manipulates codebooks rather than index streams [28], while in parallel, efficient codebook search can reduce quantization complexity without degrading quality [29]; (b) reversible data hiding in encrypted images, which creates embedding room under encryption while ensuring perfect recovery [30]; and (c) video compression–domain reversible watermarking using multi-layer embedding to raise capacity within compressed-media workflows [31].

Additionally, Liu and Zhou (2023) [32] propose a mixed multi-bit layer embedding scheme to balance embedding capacity and perceptual quality. Beyond SOC/JNC/LAS, recent compressed-domain research has further extended VQ-domain RDH in several directions: (i) lossless recompression and restoration of VQ index tables [33]; (ii) codebook-level reversible embedding that operates directly on VQ codewords rather than indices [34]; and (iii) RDH in encrypted images using intelligent predictors with additive secret sharing and joint coding [35].

In the encrypted-domain branch, VQ prediction with adaptive parametric binary-tree labeling separates embeddable pixels and increases payload while maintaining separability [5]. For HDR images, multi-MSB prediction with Huffman coding enables high-capacity RDH-EI on Radiance RGBE data [36].

• Joint Neighboring Coding (JNC)-related schemes:

Wang and Lu (2009) [16] proposed a JNC-based reversible data hiding scheme that embeds data using the difference between the current VQ index and its neighboring indices and further introduced a path-selective lossless variant within the same study. While these methods can improve embedding capacity, they may also result in higher rates.

• Locally Adaptive Coding (LAS)-related schemes:

Chang et al. (2009) [17] first introduced a LAS-based reversible data-hiding scheme for VQ indices, which adaptively reorders the index table to exploit local correlations. In another study, Ma et al. (2015) [13] developed an improved LAS (ILAS) approach that leverages the two-dimensional image structure and neighboring index correlations to achieve higher performance compared with the original LAS. More recently, Chen et al. (2024) [22] proposed an adaptive prediction-difference coding method for VQ-compressed images, which dynamically adjusts to local pixel characteristics to further enhance embedding efficiency.

• Index frequency/sorting-based schemes:

Chang et al. (2007) [18] proposed a frequency-clustering reversible data-hiding scheme, where the codebook is clustered by index-usage frequency and further partitioned into three groups via a trio-extension strategy, enabling data embedding while allowing lossless recovery of the original index table.

• Difference index-based schemes:

Li et al. (2020) [4] proposed two reversible data hiding methods, one of which innovatively constructs a difference-index table composed of differences between adjacent index values, typically containing more redundancy than standard index tables. They constructed a mapping table based on the frequency of occurrence of the difference index, achieving higher embedding capacity, and combined it with standard indexing methods to propose a joint method. This study emphasizes the idea of leveraging index differences rather than just the indices themselves to uncover more embedding potential.

• Schemes using codebooks as carriers:

Recent studies have begun to directly utilize VQ codebooks themselves as carriers of secret data, rather than merely relying on index tables. Liu et al. (2023) [37] introduced a method that embeds data by reordering the trained codebook indices, thereby exploiting redundancy in the codebook structure. Lin et al. (2024) [28] proposed a novel thresholding-based embedding scheme for VQ codebooks, in which secret data are embedded through pairwise adjustments on pixel values within codewords combined with adaptive thresholds, thereby significantly enhancing embedding capacity while maintaining reversibility. More recently, Kong et al. (2025) [23] proposed a high-fidelity reversible data hiding method based on adaptive multi-pass embedding, effectively improving embedding efficiency and visual quality. Complementing these methodological advances, Gandhi and Kumar (2025) [24] presented a comprehensive survey that provides statistical analyses, reviews current development trends, and outlines future research directions in reversible data hiding. Collectively, these works highlight the growing interest in exploiting codebook structures as effective and versatile carriers for reversible data embedding.

Deep-learning-based steganographic frameworks can achieve strong perceptual quality but typically require large-scale training and substantial computational resources. In contrast, VQ-domain schemes, including the proposed one, rely on compact IC/DC codebooks that are trained offline and do not involve neural-network training or inference during deployment, making them more practical for resource-constrained IoT environments.

1.3. Research Gap and Main Contributions

Although previous studies have made notable progress in data hiding for VQ-compressed images, particularly in increasing embedding capacity and reducing bit rates, most methods have not sufficiently addressed the degradation of image quality after VQ decompression. In many cases, irreversible schemes, or even reversible ones that introduce minor but irreparable modifications during processing, further deteriorate perceptual quality. This limitation is critical in medicine, defense, and forensic science, where high reconstruction fidelity is required.

In recent years, deep learning–based approaches for data hiding and image quality enhancement have received increasing attention. Convolutional Neural Networks (CNNs) have been applied to reversible data hiding and steganography tasks because of their ability to capture spatial correlations and model complex embedding patterns [38]. Transformer-based and GAN-driven frameworks have further improved perceptual quality, particularly in preserving high-frequency edge details [20,39]. However, these techniques generally depend on large-scale training datasets and substantial computational resources, which restrict their use in low-latency or embedded systems. This framework therefore serves as a practical solution for reversible data hiding and quality enhancement in VQ-compressed images under constrained conditions.

Building upon the aforementioned research gap, this study presents a unified framework that not only embeds secret data but also enhances the visual quality of VQ-compressed images. The main contributions of this study are summarized as follows:

• Unified Framework for Simultaneous RDH and Quality Enhancement: We propose a VQ-based framework that performs reversible data hiding and image quality enhancement without introducing additional transmission overhead, which is particularly beneficial for bandwidth-constrained and latency-sensitive networked environments such as IoT edge devices and mobile healthcare systems.
• Novel QIC Mechanism with RIV Algorithm: A Quality Improvement Code (QIC) mechanism is introduced, combining difference codebooks (DC) with the Recoding Index Value (RIV) algorithm. This mechanism embeds secret data while enhancing the perceptual quality of decompressed images by restoring lost high-frequency details in edge-marked blocks, making it highly suitable for visual data protection in distributed multimedia systems.
• Comprehensive Experimental Validation: Comprehensive experiments on ten standard test images demonstrate consistent PSNR improvements of +4 to +5.39 dB over baseline VQ methods, with SSIM gains up to +9.86% and embedding capacities approaching 100 Kbits. These results validate robustness and generalizability under varying image contents, resolutions (256 × 256, 512 × 512), and codebook sizes (64–1024). For instance, in the Zelda (512 × 512) case, SSIM improves from 94.10% to 98.23% while PSNR increases from 37.23 dB to 42.62 dB, achieving near-lossless reconstruction suitable for high-fidelity applications such as medical imaging, national defense, and forensic analysis.
• The proposed method employs compact IC/DC codebooks that are trained once offline and reused during deployment, eliminating the need for neural-network training or inference. This design minimizes computational overhead while achieving comparable or superior PSNR gains, making it well-suited for resource-constrained platforms such as wireless sensor nodes, surveillance cameras, and mobile healthcare terminals, where both real-time processing and high visual fidelity are essential.

Considering potential deployment on IoT edge devices, lightweight authenticated encryption schemes, such as the one proposed by Al-Shatari et al. [40], can complement our method by ensuring secure and efficient transmission of multimedia data. The detailed methodology and comprehensive experimental validation are presented in the following sections.

2. Materials and Methods

2.1. Framework Overview and Notation

Most existing data hiding schemes for VQ-compressed image index tables (VQ-IT) focus on embedding capacity while paying limited attention to the reconstruction quality of VQ-decompressed images. Some irreversible designs further degrade image quality after embedding. We propose a reversible data hiding (RDH) framework that simultaneously embeds secret data and enhances reconstruction quality. The key idea is to embed, along with the secret bits, a set of Quality Improvement Codes (QIC) that encode residual information to restore lost high-frequency details in the VQ-decompressed image.

Candidate embedding locations are selected by Sobel edge detection, and the threshold $T$is adaptively tuned to meet the target capacity while minimizing perceptual distortion. To facilitate the technical development that follows,

Table 1. Definitions of symbols and variables used in the proposed reversible data hiding and quality enhancement framework.

Symbol	Description	Remarks
b	Embedding rate	Number of bits embedded per block
DC	Difference Codebook	Trained on difference maps
DM	Difference Map	Pixel-wise residual between I and Ivq
DMb	Difference block	A 4 × 4 block of the difference map
ED	Required embedding capacity	Minimum number of edge-marked blocks required
ED_bits	Expanded index bits	Total number of bits required to store expanded indices after embedding (Equation (8))
I	Original image	Input grayscale test image of size M × N
i, i’	Index and recoded index	Original DC index and its recoded index using the RIV mapping, i′ = 2b× i+ s_dec
IC	Image Codebook	Generated by LBG algorithm
Ivq	VQ-decompressed image	Obtained from VQ Index Table (VQ-IT) and IC
n	Codebook size	e.g., 64, 128, 256, 512, 1024
PPR	Pure Payload Ratio	Efficiency metric, ratio of real secret bits to ED_Bits
QIC	Quality Improvement Codes	Codes that encode residual information to improve reconstruction while simultaneously carrying secret bits
r_s	Actual number of edge-marked blocks	Actual number of edge-marked blocks detected under Sobel threshold T
Real Secret Bits	Actual payload	Actual embedded secret bits = b × r_s (Equation (9))
s, s_dec	Secret bits and decimal form	Secret bit segment (s ∈ {0, 1}b); s_dec is the decimal value of s
T	Sobel threshold	Threshold parameter in Sobel edge detection, determining the number of edge-marked blocks
VQ-IT	VQ Index Table
ΔPSNR	PSNR gain	Difference vs. baseline VQ
ΔSSIM	SSIM gain	Difference vs. baseline VQ

defines the symbols and variables used throughout the paper, and Figure 1 provides a conceptual overview of the two-stage workflow (pre-processing and encoding/decoding with QIC).

2.2. Framework Overview

In the pre-processing phase, two codebooks, namely the IC and the DC, are generated and trained. The IC is constructed using all reference images, while the DC is generated from different matrices obtained via pixel-wise subtraction between each reference image and its corresponding VQ-decompressed reconstruction.

• Image Codebook (IC) Training:

The IC is trained in the complete set of reference images using VQ, a lossy image compression technique that partitions an image into blocks. Each block is then assigned to the nearest codeword in the codebook, and its index is recorded. The Linde–Buzo–Gray (LBG) algorithm, widely adopted for generating high-quality codebooks, is typically employed. Each codebook comprises a set of indices, where each index ranges from 0 to n − 1, where $n\in \left\{\mathrm{64,128,256,512,1024}\right\}$. The IC size (e.g., 256 or 512 codewords) directly impacts both the compression ratio and the perceptual quality of the decompressed image; larger codebooks generally yield higher reconstruction fidelity.

• Difference Codebook (DC) Training:

The DC is trained on all difference matrices, which represent pixel-level residuals derived from the subtraction between each reference image and its VQ-decompressed counterpart. These residuals capture compression-induced errors, which are subsequently leveraged to enhance reconstruction fidelity.

The pre-trained IC and DC serve as the foundational components for subsequent encoding and image quality enhancement processes. Image-based sensing devices are increasingly deployed across various application domains, creating a strong need for methods that protect data confidentiality while simultaneously enhancing the perceptual quality of compressed images during transmission and processing.

2.3. Encoding and Reconstruction Phase

In the proposed encoding phase, secret data are embedded within the difference domain of the image. The original image is first VQ-compressed using the IC to obtain the VQ-IT, which is then decoded to reconstruct the VQ-decompressed image. A DM is computed via pixel-wise subtraction between the original and decompressed images. Sobel edge detection is subsequently applied to the VQ-decompressed image to identify edge-marked blocks. A 4 × 4 block is classified as an edge-marked block if at least one of its pixels exceeds the Sobel gradient threshold T.

The threshold T is adaptively determined using a binary search algorithm to ensure sufficient embedding capacity while minimizing the number of modified blocks. Given the required capacity ED = ⌈|S|/b⌉, the binary search proceeds as follows: initialize T_min = 0 and T_max = 255; iteratively set T = ⌊(T_min + T_max)/2⌋ and count the edge-marked blocks |$\epsilon$|; if |$\epsilon$| < ED, decrease the threshold by setting T_max = T; if |$\epsilon$| ≥ ED, increase the threshold by setting T_min = T; repeat until |T_max − T_min| ≤ 1. The final threshold T = T_min ensures |$\epsilon$| ≥ ED with minimal over-selection, typically converging within 7–8 iterations. This adaptive strategy balances embedding capacity with perceptual quality by prioritizing the most salient edge regions for modification.

The encoding algorithm, presented as Algorithm 1, embeds secret data within the computed difference domain. The corresponding DM blocks are aligned with the identified edge-marked blocks to serve as the embedding locations. In the proposed method, the DM serves not only as the carrier of secret information but also as a means to enhance the perceptual quality of the VQ-decompressed image, particularly in edge regions where reconstruction artifacts are more perceptible.

For each selected edge block, the indices of the QIC are derived from the Difference Codebook (DC). The secret data are then embedded by re-indexing these DC values using the proposed RIV algorithm, presented as Algorithm 2. This re-indexing mechanism jointly encodes the secret bits and facilitates image quality enhancement through an optimized difference representation.

To formally describe the RIV mechanism, let I denote the original image and I_vq the VQ-decompressed image. The pixel-wise residual is defined as the difference map:

DM = I − I_vq,

(1)

The difference map DM is partitioned into non-overlapping 4 × 4 blocks, denoted as DM_b. Each block is treated as a 16-dimensional vector, which is then quantified by the Difference Codebook (DC) for both secret data embedding and quality improvement. Each difference block DM_b is vector-quantized using the DC to obtain its original index i ∈ N. Given a secret bit stream divided into segments of b bits, each segment s ∈ {0, 1}^b is converted into its decimal representation s_dec. The RIV algorithm expands the index space of DC to simultaneously encode the difference information and the secret bits. For each selected block, the recoded index i′ is computed as:

$$i\prime = 2^b \times i + s\_\mathrm{dec},$$

(2)

where 2^b defines the embedding rate and determines the index expansion factor. This mapping creates 2^b distinct sub-indices for each original codeword, enabling the embedding of b secret bits per block without introducing additional carriers.

At the receiving end, the embedded secret bits are recovered via:

s_dec = i′  mod  2^b,

(3)

and the original DC index is reconstructed by:

$$i=⌊{\displaystyle \frac{i^{\prime }}{2^b}}⌋,$$

(4)

Finally, the corresponding difference codeword DC[i] is retrieved and applied to the edge-marked blocks of I_vq, producing the enhanced reconstruction I_vq+QIC. The quality improvement is quantitatively evaluated using the peak signal-to-noise ratio (PSNR):

$$\mathrm{P}\mathrm{S}\mathrm{N}\mathrm{R}=10\cdot {\log }_{10}\left({\displaystyle \frac{MA{X}_I^2}{\mathrm{M}\mathrm{S}\mathrm{E}\left(I,{ I}_{\mathrm{v}\mathrm{q}+\mathrm{Q}\mathrm{I}\mathrm{C}}\right)}}\right)$$

(5)

where MAX_I is the maximum pixel intensity and MSE denotes the mean squared error between the original and the reconstructed images.

SSIM, on the other hand, evaluates perceptual quality by considering structural similarity, luminance, and contrast. It is computed as Equation (6):

$$\mathrm{S}\mathrm{S}\mathrm{I}\mathrm{M}\left(x,y\right)= {\displaystyle \frac{(2{\mu }_x{\mu }_y+ C_1)(2{\sigma }_{xy}+ C_2)}{({\mu }_x^2 + {\mu }_y^2 + C_1)({\sigma }_x^2 + {\sigma }_y^2 + C_2)}},$$

(6)

where ${\mu }_x$and ${\mu }_y$ are the mean intensities of images x and y, ${\sigma }_x^2$ and ${\sigma }_y^2$ are their respective variances, ${\sigma }_{xy}$ is the covariance between x and y, and $C_1$ and${ C}_2$ are small constants to stabilize the calculation. Values closer to 1 indicate higher structural fidelity and better perceptual quality.

The RIV algorithm embeds secret bits into the DC index of each selected difference block. Let b be the number of secret bits to be recorded by an index of DM edge block. Then, any codeword in DC with index value i is assigned a list of indices as $2^b\times i+k$ for 0 ≤ k ≤ 2^b − 1. For example, setting b = 2, the first index of codeword in DC (i.e., i = 0) is expanded to four indices (0, 1, 2, 3), the second index of codeword (i.e., i = 1) is expanded to four indices (4, 5, 6, 7), and so forth. If two secret bits are recoded into an index value at each iteration, then there are four different possible bit patterns denoted by these codewords at four different indices. After suitable index assignments, secret data are recoded by a new DC index. The new DC index considers secret bits to be embedded into VQ index table by any data hiding scheme.

The VQ-decompressed image, secret data, and DM indices are reconstructed in the final phase. In any VQ-IT receiver’s computer, it must have design-in firmware for both IC and DC in advance. Extract secret bits s from each index value i of DC, where s_dec = i mod 2^b, then restore the index value as $⌊{\displaystyle \frac{i}{2^b}}⌋$. Retrieve DM codewords via restored index i from DC and modify its corresponding edge-marked blocks. The codewords of DC edge-marked blocks are a set of QIC of the VQ-decompressed image. ED denotes the required embedding capacity, defined as the number of edge-marked blocks necessary to accommodate the secret bitstream S,

ED = ⌈|S|/b⌉,

(7)

The proposed framework achieves its dual objectives through the seamless integration of Algorithm 1 and Algorithm 2, where each algorithm addresses complementary aspects of the reversible data hiding and quality enhancement problem. Algorithm 1 serves as the system-level orchestrator, managing the overall workflow from image preprocessing to final output generation. It handles spatial domain operations, including VQ compression, difference map computation, and edge-based block selection. The adaptive threshold adjustment in Step 5 ensures that the embedding capacity matches the secret data requirements while prioritizing perceptually sensitive regions.

Algorithm 1. Encoding Quality Improvement Codes (QIC)
Encoding Algorithm
Input:	• Original image I ∈ ℝ(M × N) • Secret bitstream S = {s1, s2, …, s|S|} • Image Codebook IC = {c1^IC, …, c_NIC} • Difference Codebook DC = {c1^DC, …, c_iDC}
Output:	Modified VQ index table VQ-IT′ embedding secret bits and QIC
Step 1: Partition I into non-overlapping 4 × 4 blocks. Encode each block using IC to generate the VQ index table VQ-IT. Step 2: Decode VQ-IT using IC to reconstruct the VQ-decompressed image Ivq, which will be used to compute the difference map in Step 3. Step 3: Difference Map: Compute DM = I − Ivq. Step 4: Apply Sobel edge detection on Ivq to identify edge-marked blocks $\epsilon$. A 4 × 4 block is classified as an edge-marked block if at least one pixel within the block is detected as a Sobel edge point. Step 5: Adaptive Threshold Selection: Given the required embedding capacity ED = ⌈|S|/b⌉, adaptively adjust the Sobel threshold T using binary search to identify sufficient edge-marked blocks: (a) Initialize search bounds: T_min = 0 (minimum threshold), T_max = 255 (maximum threshold for 8-bit grayscale images). (b) While |T_max − T_min| > 1: i. Set T = ⌊(T_min + T_max)/2⌋ (midpoint) ii. Apply Sobel edge detection with threshold T to identify edge blocks $\epsilon$ iii. If |$\epsilon$| < ED: decrease threshold → T_max = T (need more blocks) iv. If |$\epsilon$| ≥ ED: increase threshold → T_min = T (have enough blocks) (c) Select final T = T_min ensuring |$\epsilon$| ≥ ED with minimal over-selection. Step 6: Data Embedding:     For each edge block b ∈ $\epsilon$:          (a) Extract the corresponding difference block DM_b.   (b) Call Algorithm 2 (RIV Encoding) with DM_b, DC, and secret bits s to obtain the expanded index i′ and the corresponding QIC_b. Step 7: Replace the DC indices of the selected edge-marked DM blocks in VQ-IT with the recoded indices i′ and associate them with QIC_b to generate the modified VQ-IT′ containing embedded secret bits and quality improvement codes.

Algorithm 2. Recoding Index Value (RIV)

RIV-Encoding Phase

Input:  • Difference block DM_b ∈ ℝ(4 × 4)     • Secret bitstream s ∈ {0, 1}b     • Difference Codebook DC = {c1DC,…, ciDC}     • Embedding rate b

Output: • Expanded DC index i′ ∈ [0, 2b× n − 1];     • Quality Improvement Code block QIC_b

Step 1: Convert DM_b into a 16-dimensional vector v, then find the nearest codeword: i = argmin_j ||v − cjDC||2. Step 2: Convert b-bit secret to decimal: $s_{\mathrm{d}\mathrm{e}\mathrm{c}}= \sum _{k=0}^{b-1}s\_k\times 2^k$, where s_k ∈ {0, 1}. Step 3: Compute expanded index: i′ = 2b × i + s_dec. Step 4: Retrieve QIC_b = reshape (c_iDC, 4 × 4), where i is the original DC index obtained in Step 1 (distinct from the recoded index i’ in Step 3). Step 5: Return i′ and QIC_b.

RIV-Decoding Phase

Input:     • Expanded DC index i′ ∈ [0, 2b× n − 1]     • Difference Codebook DC     • Embedding rate b

Output: Recovered secret bits s ∈ {0, 1}b and Quality Improvement Code block QIC_b

Step 1: Secret Bits Recovery: s_dec = i′ mod 2b.     Convert s_dec to binary: s = binary (s_dec, b), s is the recovered b-bit secret segment. Step 2: Original DC Index Reconstruction: $i=⌊{\displaystyle \frac{i^{\prime }}{2^b}}⌋$. Step 3: Extract QIC_b = reshape (c_iDC, 4 × 4) using the restored original DC index i, rather than the expanded index i’. Step 4: Return s and QIC_b.

Algorithm 2 operates at the block level, implementing the core RIV mechanism for individual difference blocks. When invoked by Algorithm 1 (Step 6), Algorithm 2 processes each selected difference block DM_b to produce expanded indices that simultaneously carry secret information and enable quality enhancement through the recovered QIC.

The interaction between the two algorithms follows a producer-consumer pattern. Algorithm 1 identifies and prepares candidate blocks (producer), while Algorithm 2 processes these blocks to generate embedded indices (consumer). This design enables parallel processing of multiple blocks when computational resources permit, further improving efficiency for large-scale image processing. The two-algorithm structure provides natural checkpoints for error detection and recovery. Algorithm 1 can validate that sufficient edge blocks are available before invoking Algorithm 2, preventing runtime failures. Similarly, Algorithm 2 can verify that expanded indices remain within valid ranges, ensuring compatibility with downstream processing components. This modular approach facilitates algorithm verification, performance optimization, and future extensions to different compression domains or embedding strategies.

The overall computational complexity of the proposed framework is O(W × H + |$\epsilon$| × log(n)), where W × H represents the image processing overhead and |$\epsilon$| × log(n) accounts for the DC codebook search operations on edge-marked blocks. Since |$\epsilon$| ≪ W × H/16, indicating that only a small fraction of blocks is selected for embedding, the additional overhead for quality enhancement remains minimal, making the approach suitable for resource-constrained applications.

3. Experiments

3.1. Experimental Setup and Dataset Description

All experiments in this study were performed on the following hardware and software configuration:

• Hardware: Intel Core i7-12700H CPU (Intel Corporation, Santa Clara, CA, USA), 16 GB RAM
• Operating System: Windows 10/11 64-bit (Microsoft Corporation, Redmond, WA, USA)
• Programming Environment: Python 3.12 (Python Software Foundation, https://www.python.org)
• Python Libraries:

  ○

  NumPy 1.26.4 (https://numpy.org)

  ○

  OpenCV-Python 4.10.0.84 (https://github.com/opencv/opencv-python), accessed on 10 November 2025

  ○

  scikit-image 0.23.2 (https://scikit-image.org)

To establish a fair and comprehensive evaluation environment, we adopt ten widely used grayscale benchmarks—Baboon, Boat, Jet, Sailboat, Lena, Zelda, House, Pepper, Family, and Tiffany—shown in Figure 2a–j. Each image is tested at two spatial resolutions (256 × 256 and 512 × 512) so that performance can be analyzed under both low- and high-resolution conditions commonly encountered in edge/IoT scenarios.

All images are partitioned into non-overlapping 4 × 4 blocks and represented as 16-dimensional vectors for vector quantization. Two codebooks are used: the Image Codebook (IC) and the Difference Codebook (DC). Unless otherwise stated, the IC/DC codebooks are trained once (on the full pool of block vectors) and reused for all test images to ensure comparability across conditions. To examine the impact of codebook granularity, we consider five sizes for both IC and DC: {64, 128, 256, 512, 1024} codewords. These configurations capture the typical trade-off between compression efficiency (smaller codebooks) and reconstruction fidelity (larger codebooks) while keeping the processing pipeline fixed.

Edge-aware embedding is controlled by sweeping the Sobel threshold $T\in \left\{\mathrm{10,30,50,70,90,110,130}\right\}$,which selects perceptually sensitive (edge) blocks for QIC-assisted refinement. The payload per selected block is governed by the number of embedded bits $b\in \{\mathrm{1,2},\mathrm{3,4},\mathrm{5,6}\}$. This design explicitly separates the effects of codebook size (IC/DC), edge sensitivity ($T$), and payload ($b$).

The factorial matrix comprises 10 images × 2 resolutions × 5 IC sizes × 5 DC sizes = 500 base conditions. For each base condition, we evaluate 7 threshold settings $T$ and 6 embedding settings $b$, yielding 21,000 total runs. All experiments are assessed with the same metrics—PSNR and SSIM—under a consistent pipeline to enable apples-to-apples comparisons across image content, resolution, and codebook complexity.

For brevity in the main tables,

Table 2. Effect of Sobel thresholds on embedding capacity and reconstruction quality for Zelda image (512 × 512).

IC/DC Size	Sobel Threshold	Edge-Marked Blocks	Real Secret Bits	ED_Bits	VQ PSNR (dB)	VQ SSIM (%)	PSNR of Proposed (dB)	SSIM of Proposed (%)	ΔPSNR	ΔSSIM
64	10	15,107	90,642	181,284	33.12	86.50	37.44	94.43	4.32	7.93%
	30	14,321	85,926	171,852	33.12	86.50	37.35	94.30	4.23	7.79%
	50	8667	52,002	104,004	33.12	86.50	36.36	91.85	3.25	5.35%
	70	5927	35,562	71,124	33.12	86.50	35.75	90.44	2.64	3.94%
	90	3319	19,914	39,828	33.12	86.50	34.93	88.77	1.82	2.26%
	110	2637	15,822	31,644	33.12	86.50	34.66	88.29	1.54	1.79%
	130	1680	10,080	20,160	33.12	86.50	34.20	87.61	1.08	1.10%
256	10	15,696	94,176	219,744	35.20	90.91	40.33	97.10	5.12	6.19%
	30	11,985	71,910	167,790	35.20	90.91	39.73	96.19	4.53	5.29%
	50	7672	46,032	107,408	35.20	90.91	38.68	94.57	3.48	3.67%
	70	4675	28,050	65,450	35.20	90.91	37.68	93.14	2.48	2.23%
	90	2943	17,658	41,202	35.20	90.91	36.97	92.31	1.77	1.40%
	110	1982	11,892	27,748	35.20	90.91	36.53	91.85	1.32	0.94%
	130	1332	7992	18,648	35.20	90.91	36.19	91.54	0.99	0.64%
1024	10	16,082	96,492	257,312	37.23	94.10	42.62	98.23	5.39	4.12%
	30	11,324	67,944	181,184	37.23	94.10	41.84	97.42	4.61	3.32%
	50	6388	38,328	102,208	37.23	94.10	40.49	96.13	3.26	2.03%
	70	3776	22,656	60,416	37.23	94.10	39.59	95.37	2.36	1.27%
	90	2653	15,918	42,448	37.23	94.10	39.09	95.01	1.86	0.90%
	110	1820	10,920	29,120	37.23	94.10	38.66	94.74	1.43	0.63%
	130	1255	7530	20,080	37.23	94.10	38.30	94.55	1.07	0.44%

and

Table 3. Effect of Sobel thresholds on embedding capacity and reconstruction quality for Zelda image (256 × 256; b = 6).

IC/DC Size	Sobel Threshold	Edge-Marked Blocks	Real Secret Bits	ED_Bits	VQ PSNR (dB)	VQ SSIM (%)	PSNR of Proposed (dB)	SSIM of Proposed (%)	ΔPSNR	ΔSSIM
64	10	3991	23,946	47,892	29.32	82.30	32.92	92.16	3.60	9.86%
	30	3896	23,376	46,752	29.32	82.30	32.88	92.04	3.57	9.74%
	50	3254	19,524	39,048	29.32	82.30	32.65	90.95	3.34	8.65%
	70	2753	16,518	33,036	29.32	82.30	32.41	89.91	3.10	7.61%
	90	1924	11,544	23,088	29.32	82.30	31.86	87.81	2.54	5.51%
	110	1634	9804	19,608	29.32	82.30	31.60	87.01	2.29	4.71%
	130	1141	6846	13,692	29.32	82.30	31.06	85.49	1.74	3.20%
256	10	4038	24,228	56,532	30.98	87.50	35.02	95.03	4.04	7.53%
	30	3680	22,080	51,520	30.98	87.50	34.92	94.64	3.94	7.14%
	50	3047	18,282	42,658	30.98	87.50	34.64	93.71	3.66	6.21%
	70	2406	14,436	33,684	30.98	87.50	34.23	92.53	3.25	5.03%
	90	1749	10,494	24,486	30.98	87.50	33.68	91.26	2.70	3.76%
	110	1282	7692	17,948	30.98	87.50	33.24	90.38	2.26	2.88%
	130	981	5886	13,734	30.98	87.50	32.88	89.74	1.90	2.24%
1024	10	4079	24,474	65,264	32.43	91.20	36.57	96.53	4.14	5.32%
	30	3614	21,684	57,824	32.43	91.20	36.48	96.21	4.04	5.01%
	50	2909	17,454	46,544	32.43	91.20	36.18	95.48	3.75	4.27%
	70	2135	12,810	34,160	32.43	91.20	35.71	94.58	3.28	3.38%
	90	1575	9450	25,200	32.43	91.20	35.25	93.85	2.81	2.64%
	110	1203	7218	19,248	32.43	91.20	34.85	93.31	2.42	2.10%
	130	935	5610	14,960	32.43	91.20	34.52	92.93	2.09	1.72%

report three representative IC/DC sizes (64/256/1024) that summarize the observed trends; the complete 5 × 5 IC/DC grid (all five sizes) exhibits consistent behavior with the reported results.

3.2. Embedding Capacity and Payload Analysis

To evaluate the overall impact of the proposed data hiding mechanism on the VQ index space, we introduce two complementary metrics. The first is the Expanded Index Bits (ED_Bits), which denotes the total number of bits required to store the modified index table after embedding, incorporating both secret bits and the overhead caused by index expansion. The second is the Real Secret Bits, which quantifies the actual amount of embedded confidential data.

While the recoding mechanism expands each original index to accommodate secret bits—thus increasing the bit length per index—the true embedding capacity remains dependent on the number of edge-marked blocks and the number of secret bits assigned per block. Accordingly, the total number of bits needed to represent all expanded indices is defined as:

$$\mathrm{ED}\_\mathrm{Bits} = ⌈\left({log}_2 \left(2^b\times n\right)\right)\times r\_s⌉,$$

(8)

where b denotes the number of embedded secret bits per index; n is the size of the Difference Codebook (DC), and r_s represents the number of edge-marked blocks selected for embedding (i.e., effective embedding indices). These indices correspond to the edge-marked blocks identified by Sobel edge detection and are directly proportional to the embedding capacity, r_s is dynamically determined by the Sobel threshold T. When T decreases, more edge-marked blocks are detected (larger r_s); when T increases, fewer edge-marked blocks are detected (smaller r_s). The product b × r_s directly corresponds to the Real Secret Bits reported in Table 1. The term ${\mathit{log}}_2(2^b\times n)$ corresponds to the bit-length required to represent the expanded index space [0, 2^b $\times$ n − 1], which directly follows from the RIV mapping as Equation (2). In contrast, the actual secret bits embedded into the VQ index table are given by:

$$\mathrm{R}\mathrm{e}\mathrm{a}\mathrm{l} \mathrm{S}\mathrm{e}\mathrm{c}\mathrm{r}\mathrm{e}\mathrm{t} \mathrm{B}\mathrm{i}\mathrm{t}\mathrm{s}=b \times r\_s,$$

(9)

For a more intuitive performance evaluation, we define the pure payload ratio (PPR), which measures embedding efficiency as the proportion of meaningful secret data to total index storage cost and is formulated as:

$$\mathrm{P}\mathrm{u}\mathrm{r}\mathrm{e} \mathrm{P}\mathrm{a}\mathrm{y}\mathrm{l}\mathrm{o}\mathrm{a}\mathrm{d} \mathrm{R}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}(\mathrm{P}\mathrm{P}\mathrm{R})= {\displaystyle \frac{b}{⌈{log}_2(2^b\times n)⌉}}$$

(10)

The theoretical PPR values under different combinations of b and n. As observed, the PPR increases with higher b values, reflecting more efficient use of the expanded index space. However, increasing b may also affect image quality, indicating a trade-off that should be carefully managed. In practice, selecting an optimal b requires balancing payload efficiency and distortion constraints. Although the PPR is not directly reported in the experimental results, its theoretical formulation offers a valuable reference for understanding the trade-off between embedding capacity and structural overhead.

To further investigate this, we conducted comparative experiments between fixed and variable b-value settings. In the variable-b approach, the system dynamically adjusts b based on the detected number of edge-marked blocks and the desired capacity. This adaptive scheme may lead to higher efficiency in scenarios with uneven edge distribution or bandwidth-constrained IoT environments.

3.3. Experimental Results

Table 2 and Table 3 present the quantitative evaluation of the proposed framework on the Zelda image at two spatial resolutions (512 × 512 and 256 × 256), under varying Sobel edge detection thresholds T (10–130) with a fixed embedding rate of b = 6. For each resolution, three codebook configurations (IC/DC = 64, 256, and 1024) were examined. The reported metrics include ED_Bits—the theoretical maximum number of expanded index bits required to represent Sobel-detected edge blocks—as well as the corresponding quality gains in PSNR and SSIM (ΔPSNR and ΔSSIM) over the baseline VQ-decompressed image. Here, ED_Bits denotes the total number of expanded index bits after embedding, as defined in Equation (8), while Real Secret Bits represent the actual embedded payload, as defined in Equation (9).

At lower T values, a larger number of edge-marked blocks are detected, resulting in higher embedding capacities and more substantial quality improvements. For example, in Table 2 (512 × 512 resolution), the configuration IC/DC = 1024 at T = 10 increases PSNR from 37.23 dB to 42.62 dB (ΔPSNR = 5.39 dB) and SSIM from 94.10% to 98.22% (ΔSSIM = 4.12%), with an embedding capacity of 96,492 bits. However, at T = 130, capacity drops sharply to 7530 bits, and quality gains reduce to 1.07 dB in PSNR and 0.44% in SSIM. Similar trends are observed in Table 3 (256 × 256 resolution), where capacities are lower due to fewer available blocks. For example, IC/DC = 1024 at T = 10 achieves a capacity of 24,474 bits—approximately one quarter of the high-resolution case—while still increasing PSNR from 32.43 dB to 36.57 dB (ΔPSNR = 4.14 dB) and SSIM by 5.32%. The largest proportional SSIM gain in Table 3 is recorded for IC/DC = 64 at T = 10, where SSIM improves from 92.16% to 98.04% (ΔSSIM = 9.86%) alongside a PSNR gain of 3.60 dB.

For each experiment, the Sobel threshold T was preset, and r_s represents the resulting number of detected edge blocks. In practice, T would be adaptively adjusted to meet the required embedding capacity ED for a given secret message. The combined table and figure analysis confirms that the proposed approach offers consistent and substantial improvements over baseline VQ decompression in both objective metrics and embedding capacity. These benefits are maximized when fine edge structures are retained through lower Sobel thresholds, a finding that holds across different codebook sizes and image resolutions. For a more intuitive performance evaluation, we define the pure payload ratio (PPR), which measures embedding efficiency. For example, when the IC/DC codebook size is n = 256 and the embedding rate is b = 6, the PPR calculation proceeds as follows:

Step 1: Calculate the expanded index space size:

Expanded index space = 2^b × n = 2⁶ × 256 = 64 × 256 = 16,384.

Step 2: Calculate the required bits to represent this space:

$${log}_2\left(\mathrm{16,384}\right)={log}_2\left(2^{14}\right)=14 \mathrm{b}\mathrm{i}\mathrm{t}\mathrm{s}.$$

Step 3: Apply the PPR formula:

$$\mathrm{P}\mathrm{P}\mathrm{R}={\displaystyle \frac{b}{{log}_2\left(2^b\times n\right)}}= {\displaystyle \frac{6}{14}} \approx 0.4286.$$

This result indicates that under these settings (b = 6, n = 256), approximately 42.86% of the total embedding capacity is utilized for carrying real secret bits, while the remaining 57.14% represents structural overhead required by the RIV mechanism.

The trends in Table 2 and Table 3 are visually confirmed in Figure 3a–d, where the PSNR and SSIM curves of the proposed method consistently lie above those of baseline VQ across all thresholds. The separation is greatest at low T values, particularly for large codebooks, while the IC/DC = 1024 configuration shows a steeper decline in gains as T increases—indicating its higher sensitivity to edge suppression. In lower-resolution cases, the relative SSIM improvement is most pronounced for smaller codebooks (IC/DC = 64), despite their lower absolute PSNR gains. In both resolutions, the curves confirm that preserving a larger number of edge-marked blocks yields more substantial quality improvements. These quantitative patterns are further analyzed in Figure 4, which examines the relationship between ΔPSNR and PPR across different T values for both resolutions. As T increases, both ΔPSNR and PPR decrease monotonically, reflecting the trade-off between embedding capacity and reconstruction quality. Larger codebooks (IC/DC = 1024) provide the highest ΔPSNR at low T but experience the most rapid quality drop with increasing threshold. Medium-sized codebooks (IC/DC = 256) offer a more balanced trade-off, maintaining stable performance over a wider range of T values. This analysis, combined with the results from Table 2 and Table 3 and Figure 3, confirms that the proposed QIC framework delivers consistent quality improvements, with optimal performance achieved when enough high-frequency edge blocks are retained for enhancement and data embedding.

3.4. Visual Quality Enhancement

3.4.1. Experiments on Grayscale Images

Figure 5 compares the baseline VQ-decompressed images with the enhanced reconstructions generated by the proposed QIC-based method under fixed parameters (image size = 256 × 256, IC size = 512, DC size = 512, T = 10, embedding rate b = 5), using the House and Baboon test images. In the House image (Figure 5a,b), the red-boxed roof region clearly demonstrates a substantial improvement in visual quality. The baseline VQ result exhibits noticeable block artifacts along the roof edges and significant texture loss on the wall surface, whereas the proposed method effectively restores the linearity of the roof contours and recovers finer brick and window details, resulting in a more natural and realistic structure. This improvement is reflected in the PSNR increase from 26.47 dB to 29.52 dB (ΔPSNR = 3.05 dB), and in the SSIM increase from 83.09% to 91.11%, representing a 9.65% improvement. In the Baboon image (Figure 5c,d), the red-boxed eye region shows that the proposed method produces clearer iris boundaries and reduces pixelation around the eyelids. In the cheek fur region, also marked in red, the baseline VQ image suffers from coarse quantization noise, whereas the proposed method reconstructs smoother luminance gradients and sharper fur details. These enhancements correspond to a PSNR increase from 22.58 dB to 24.95 dB (ΔPSNR = 2.37 dB), and an SSIM increase from 67.85% to 82.97%, representing a 22.28% improvement.

In Figure 6, it can be observed that Real Secret Bits (green curve) increase consistently with larger DC sizes, ranging from 51,543 at DC size 64 to 73,411 at DC size 1024. This indicates that larger DC sizes contribute to a greater amount of actual embedded data. On the other hand, ED Bits (blue curve) show relatively stable values across different DC sizes, fluctuating slightly around 16,700 to 17,100, suggesting that the theoretical embedding capacity is relatively unaffected by changes in DC size under the current configuration. Meanwhile, the PPR (orange dashed line) exhibits a gradual decline as DC size increases—from 0.333 to 0.231—indicating that although the total embedded data increases, the embedding efficiency per pixel decreases, likely due to the larger context blocks distributing the payload over more pixels.

Figure 7, Figure 8 and Figure 9 present a visual comparison between the VQ-decompressed images and those enhanced by our proposed method, along with their corresponding edge maps, under the same experimental conditions (image size: 512 × 512, IC/DC size = 512, Sobel threshold T = 50). In each figure, subfigure (a) shows the VQ-decompressed image, while (b) presents the enlarged edge map extracted from the same VQ-decompressed image. In (b), the edges appear discontinuous and suffer from visible blocking artifacts, with fine structural details—such as aircraft markings in Jet, hat contours in Lena, and mast/rigging details in Sailboat—appearing blurred or partially lost. Subfigure (c) displays the image reconstructed using our proposed method, which effectively suppresses blocking artifacts and enhances edge continuity. Subfigure (d) shows the enlarged edge map of the enhanced image, where edges are noticeably sharper, continuous, and better aligned with the underlying object boundaries. For example, in Figure 7d, the “F-16” tail marking becomes more legible; in Figure 8d, the curved rim of Lena’s hat is smoother and cleaner; and in Figure 9d, the sail edges and mast are more clearly defined without distortion. Quantitatively, for the Jet image (Figure 7), the PSNR improves from 32.01 dB to 35.71 dB; for the Lena image (Figure 8), from 30.99 dB to 34.22 dB; and for the Sailboat image (Figure 9), from 29.63 dB to 32.69 dB. These results confirm that the proposed method consistently improves both the visual quality and structural fidelity of VQ-decompressed images, particularly in preserving fine details in edge regions.

Figure 10 illustrates the PSNR results of different test images under the condition of T = 10 with codebook sizes n = 64 and n = 128. The solid lines represent the proposed method, while the dashed lines correspond to conventional VQ. It can be clearly observed that the proposed method consistently improves the PSNR across all test images, with the curves of the proposed method shifted upward compared to those of VQ, indicating significant quality enhancement. As the codebook size increases from 64 to 128, the PSNR values of both VQ and the proposed method increase, demonstrating that a larger codebook captures more image features and leads to better reconstruction quality. Among the test images, House, Zelda, and Tiffany exhibit particularly noticeable improvements, suggesting that the proposed method is especially effective in preserving details and high-frequency information. Figure 11 presents the PSNR performance for larger codebook sizes (n = 256, 512, and 1024). Like Figure 10, the solid lines denote the proposed method and the dashed lines represent conventional VQ. The results show that the proposed method consistently outperforms VQ across all test images, and the PSNR increases steadily as the codebook size grows. Challenging images such as Baboon exhibit relatively smaller gains, while images like House, Zelda, and Tiffany achieve more notable improvements. These findings confirm that the proposed QIC-based scheme is effective across both small and large codebook configurations and achieves a favorable balance between reconstruction quality and representational capacity.

The PSNR values also rise, reflecting the capability of a larger codebook to further enhance reconstruction quality. Notably, for images such as Zelda and Tiffany, the PSNR achieved by the proposed method exceeds 38 dB, demonstrating near high-quality reconstruction. Even for more challenging images with complex textures, such as Baboon, where the baseline PSNR is relatively low, the proposed method still provides a steady improvement.

To ensure a fair comparison, we provide a brief summary of the experimental settings for the schemes being compared. Wang and Lu (2009) [16] proposed a path-optional lossless scheme based on joint neighboring coding (JNC), which was evaluated on standard 512 × 512 grayscale test images (e.g., Lena, Baboon, Pepper) with a block size of 4 × 4 and a codebook size of 512. Zhao et al. (2014) [2] introduced a two-stage VQ (TSVQ)-based reversible data hiding framework, which also adopted 512 × 512 images under comparable codebook settings. Chang et al. (2021) [41] presented a two-layer scheme that combines declustering and indicator-free search-order coding (IFSOC), in which the experiments employed a block size of 4 × 4 with codebook sizes ranging from 256 to 1024. For our proposed method, all experiments were consistently conducted using 512 × 512 grayscale images, a block size of 4 × 4, a codebook size of 512, and an embedding rate fixed at b = 6.

As summarized in

Table 4. Performance comparison with existing VQ-based reversible data hiding methods.

Images	Metrics	Wang & Lu (2009) [16]	Chang et al. (2021) [41]	Zhao et al. (2014) [2]	Our Proposed
LENA	PSNR (dB)	31.22	30.66	32.26	33.88
	Payload/EC (bits)	32,004	63,299	64,008	90,258
Baboon	PSNR	23.89	25.59	24.73	27.82
	Payload/EC (bits)	47,250	47,069	64,008	98,010
Pepper	PSNR	30.56	30.49	31.74	35.47
	Payload/EC (bits)	47,250	68,412	64,008	91,350

and illustrated in Figure 11, prior VQ-based RDH schemes demonstrate a clear trade-off between image quality and embedding capacity. For example, Wang and Lu (2009) [16] achieved 31.22 dB PSNR with 32,004 bits on Lena and only 23.89 dB with 47,250 bits on Baboon, while Zhao et al. (2014) [2] reported 32.26 dB and 64,008 bits on Lena, and Chang et al. (2021) [41] achieved 30.66 dB with 63,299 bits. By contrast, the proposed RIV + QIC framework consistently outperforms all baselines, achieving 33.88 dB and 90,258 bits on Lena, 35.47 dB and 91,350 bits on Pepper, and 27.82 dB with 98,010 bits on Baboon. Unlike conventional schemes that deteriorate significantly as payloads increase, the integration of Quality Improvement Codes (QIC) enables simultaneous enhancement of visual fidelity and expansion of payload capacity. These results clearly validate the feasibility and superiority of the proposed method in achieving a more effective balance between imperceptibility and embedding performance.

3.4.2. Experiments on Color Images

To further validate the effectiveness of the proposed QIC framework, we extended our experiments to color images by applying the method to the luminance (Y) channel while preserving the chrominance components (Cb and Cr) unchanged. Two widely used benchmark color images—Lena and Baboon (512 × 512 pixels)—were selected for evaluation. The codebook size was set to n $=1024$, the embedding depth $b=2$, and the Sobel edge threshold $T=180$. This configuration ensures that chrominance information remains lossless, while both quality enhancement and reversible data embedding are performed exclusively on channel Y.

• Experimental Results for Lena

Figure 12a–c illustrates the reconstruction results for the Lena image. The original RGB image (Figure 12a) exhibits smooth facial features and rich textural details. After standard VQ compression ($n=1024$), the reconstructed image (Figure 12b) achieved PSNR = 31.82 dB and SSIM = 88.6%, with noticeable blocking artifacts in smooth regions. Using the proposed QIC method (Figure 12c), the image quality improved to PSNR = 32.97 dB and SSIM = 89.5%, representing ΔPSNR = +1.15 dB and ΔSSIM = +0.9%, while simultaneously embedding reversible secret data.

The edge selection algorithm identified 2564 edge blocks (15.65% of 16,384 total blocks), which were used for both quality enhancement and data hiding. This moderate ratio corresponds to Lena’s smooth background and facial areas. Extraction verification confirmed 100% accuracy in data recovery, demonstrating the perfect reversibility of the RIV mechanism.

• Experimental Results for Baboon

Figure 12d–f shows the reconstruction results for the Baboon image, which is rich in high-frequency textures. The baseline VQ reconstruction (Figure 12e) produced PSNR = 28.85 dB and SSIM = 87.1%, significantly lower than Lena due to its intricate texture patterns. Applying QIC (Figure 12f) raised the quality to PSNR = 30.09 dB and SSIM = 89.0%, yielding ΔPSNR = +1.24 dB and ΔSSIM = +1.9%. Visual inspection shows clearer fur texture and sharper details, as the differential codebook (DC) effectively compensates for VQ quantization loss.

A total of 4671 edge blocks (28.52%) were detected, nearly twice that of Lena, reflecting higher texture density. Despite the increased embedding capacity, extraction accuracy remained 100%, confirming the robustness of the QIC framework in complex image structures.

3.4.3. Analysis and Discussion

The experimental findings on color images highlight several advantages of the proposed QIC framework:

• Consistent Quality Enhancement—Both test images exhibit steady PSNR gains of 1.15–1.24 dB and SSIM improvements of ≈ 0.009, achieved without additional transmission overhead since QIC information is embedded within IC indices.
• Adaptive Edge Utilization—The edge detection process automatically adapts to image complexity, selecting fewer edge blocks for smooth content (Lena) and more for textured scenes (Baboon).
• Color Fidelity—Since only the luminance channel is processed, chrominance information remains unaltered. SSIM values above 0.89 confirm that color fidelity and perceptual similarity are well preserved.

Overall, the results demonstrate that the proposed QIC framework generalizes effectively to color images, maintaining the dual benefits of quality enhancement and reversible data hiding while adapting dynamically to different texture characteristics.

3.5. Performance Analysis and Trade-Off Discussion

While the proposed method achieves PSNR gains of +4 to +5.39 dB over baseline VQ decompression, it is important to contextualize these results within the broader landscape of image quality enhancement and data hiding methods. Recent deep learning approaches, particularly CNN-based and Transformer-based models [38,39], have demonstrated the capability to achieve higher absolute PSNR values, often exceeding 40–45 dB on similar test images. However, a direct PSNR comparison without considering computational cost, deployment feasibility, and embedding capacity would be incomplete and potentially misleading. The fundamental advantage of the proposed framework lies in its unique combination of multiple desirable properties that are rarely achieved simultaneously in existing methods:

• Pre-training Architecture with Zero Computational Overhead: Unlike deep learning methods that require extensive training on large datasets (often 10,000+ images) and GPU inference, the proposed QIC framework operates purely through codebook lookup and algebraic operations. The computational complexity O(W × H + |$\epsilon$| × log(n)) is dominated by standard VQ encoding, with the additional QIC embedding introducing negligible overhead. For a 512 × 512 image with codebook size n = 512 and approximately 16,000 edge blocks, the total processing time on a standard CPU (Intel Core i7) is approximately 0.3 s, compared to 2–5 s for typical CNN-based methods requiring GPU acceleration. This makes the method immediately deployable on resource-constrained IoT devices, wireless sensor nodes, and edge cameras without requiring hardware upgrades or model retraining.
• Simultaneous Data Hiding and Quality Enhancement: A critical distinguishing feature is that the proposed method achieves two objectives simultaneously: (1) embedding up to 100 Kbits of secret data, and (2) improving visual quality over standard VQ decompression. In contrast, most deep learning image enhancement methods focus solely on quality improvement without data hiding capability. When data hiding is introduced into deep learning frameworks, it typically degrades image quality rather than enhancing it. The QIC mechanism uniquely leverages the residual information for dual purposes—the same difference codewords that carry secret bits also restore high-frequency edge details. This synergy is not achievable in conventional approaches that treat data hiding and quality enhancement as separate, competing objectives.
• No Additional Transmission Overhead: The proposed framework embeds both secret data and quality improvement codes within the existing VQ index table structure without increasing file size or transmission bandwidth. The RIV mechanism expands the index space mathematically (from n to 2^b × n) but does not require transmitting additional auxiliary information. In comparison, many high-PSNR enhancement methods require transmitting residual maps, attention masks, or auxiliary networks, significantly increasing bandwidth requirements—a critical constraint in IoT and mobile applications where network resources are limited.
• Guaranteed Reversibility and Lossless Secret Recovery: The proposed method ensures perfect recovery of both the original VQ indices and the embedded secret data through the invertible RIV mapping (Equations (3) and (4)). This property is essential for applications in medical imaging, forensic analysis, and legal documentation where any loss of embedded authentication or metadata is unacceptable. Many deep learning steganography methods, despite achieving high visual quality, suffer from imperfect secret recovery (bit error rates of 0.1–1%) due to quantization and rounding errors in neural network operations.
• Embedding Capacity and Efficiency: The proposed method achieves embedding capacities of 90,000–100,000 bits on 512 × 512 images, substantially higher than typical VQ-based methods (32,000–64,000 bits as shown in Table 4). More importantly, the Pure Payload Ratio (PPR) of approximately 43% (for b = 6, n = 256) indicates that nearly half of the transmitted bits carry actual secret information, with the remainder representing structural overhead. This efficiency is comparable to or better than many existing VQ-based schemes while simultaneously providing a quality improvement combination not achieved by prior work.
• Scalability and Adaptability: The method’s performance scales predictably with codebook size and Sobel threshold, as demonstrated in Table 2 and Table 3 and Figure 3 and Figure 4. This predictability enables system designers to precisely balance quality, capacity, and computational cost based on application requirements. For instance, in bandwidth-critical scenarios, smaller codebooks (n = 64) can be used with acceptable quality (ΔPSNR ≈ +4 dB), while high-fidelity applications can employ larger codebooks (n = 1024) for near-lossless reconstruction (ΔPSNR ≈ +5.39 dB). Such flexibility is difficult to achieve in deep learning methods, where model architecture changes require complete retraining.
• Trade-off Analysis: It is acknowledged that for applications where absolute PSNR maximization is the sole objective and computational resources are unconstrained, deep learning methods may achieve 2–3 dB higher PSNR than the proposed approach. However, for the target application domain—resource-constrained IoT devices requiring simultaneous secure data embedding and quality enhancement with minimal computational and transmission overhead—the proposed method offers a more favorable trade-off. The combination of pre-training operation, zero transmission overhead, guaranteed reversibility, high embedding capacity, and substantial quality improvement (ΔPSNR +4 to +5.39 dB, ΔSSIM +4% to +10%) makes the framework particularly well-suited for practical deployment in surveillance systems, mobile healthcare terminals, and defense communication networks.

Furthermore, the proposed method is complementary rather than competitive with deep learning approaches. Future hybrid architectures could integrate QIC-based embedding with lightweight neural enhancement modules, combining the efficiency and reversibility of the former with the perceptual quality of the latter. Such hybrid designs represent a promising direction for balancing the multiple competing constraints inherent in real-world multimedia security systems.

3.6. Robustness Under Noisy Conditions and JPEG Compression

The evaluation protocol is as follows. The input images were first subjected to various perturbations, including clean conditions, Gaussian noise (σ ∈ {5, 10, 20}), and salt-and-pepper (S&P) noise with densities of {1%, 3%}. They were then processed using JPEG (Q = 50), baseline VQ (n = 256), and the proposed QIC method (n = 256, b = 3). PSNR and SSIM were computed with respect to the clean reference image. Results in Figure 13 are averaged over Lena512 and Zelda512, with one curve representing each method.

The main findings are summarized below:

• Under low-noise conditions, all methods perform comparably.
• Under medium-to-heavy noise (e.g., σ = 20, S&P = 3%), JPEG exhibits noticeable degradation—particularly in SSIM—with visible blocking artifacts.
• QIC maintains stable performance across all noise levels and achieves higher SSIM than JPEG and VQ under noisy conditions, while its PSNR remains competitive with the best baseline.
• Unlike JPEG or VQ, QIC provides both reversible embedding and structural enhancement within a single, unified pipeline.

Overall, these results demonstrate that QIC demonstrates greater resilience to noise while maintaining low deployment complexity. Although JPEG is computationally lightweight, it lacks support for reversible embedding and structural enhancement. On CPU-only execution with n = 256 and b = 3, the full QIC pipeline requires 4.67 ± 0.25 s per image (ranging from 4.41 to 4.99 s across noise conditions). This trade-off is acceptable for edge-device scenarios where robustness and interpretability are critical, such as medical or surveillance imagery. At deployment, QIC requires no deep-learning training or test-time adaptation; it operates solely with pre-trained IC/DC VQ codebooks and lightweight local operations for indexing and reconstruction.

3.7. Runtime Evaluation

We evaluated computational efficiency in a CPU-only setting using the same processing pipeline described in Section 3.6. Unless otherwise noted, the timings exclude disk I/O so that the reported values reflect algorithmic latency rather than storage overhead. With the configuration fixed at $n=256$ and $b=3$, the baseline vector quantization (VQ) stage requires 0.466 s per image on average. When the complete QIC pipeline is enabled—comprising edge-threshold sweeping, enhancement/reconstruction, and reversible embedding—the average latency is $4.67\pm 0.25$ s per image, ranging from 4.41 to 4.99 s across the tested noise conditions.

For context, we also measured in-memory JPEG (Q = 50) encoding plus decoding. This micro-benchmark yields $0.00073\pm 0.0004$ s per image, which reflects codec computation only; it excludes disk I/O and any embedding or enhancement stages. As a result, the end-to-end throughput of JPEG-based pipelines will be higher than this micro-benchmark once file operations and additional processing are included.

In terms of raw codec speed, JPEG is the fastest, followed by VQ, and then QIC is the slowest. This ordering is expected because QIC performs substantially more work than pure compression and decompression. However, JPEG and baseline VQ do not provide reversible data embedding or structural enhancement. When comparing functionally equivalent workflows, QIC executes the entire sequence on the CPU with stable, predictable latency, combining compression with reversible embedding and robustness-oriented enhancement. This profile is appropriate for edge and IoT scenarios that prioritize robustness and interpretability over maximum frame rate.

Finally, we clarify the training assumption: at deployment, QIC requires no neural-network training or test-time learning. The method relies on fixed IC/DC VQ codebooks learned once offline, and runtime computation consists of codebook indexing and deterministic local operations. This design mitigates the variability and hardware dependencies associated with learned inference while providing the capabilities required for reversible embedding and noise-robust structural enhancement.

4. Conclusions and Future Work

In this study, we introduced a unified reversible data hiding (RDH) framework for VQ-compressed images that leverages Quality Improvement Codes (QIC) and the Re-coding Index Value (RIV) mechanism to simultaneously achieve secure data embedding and visual quality enhancement. Unlike existing VQ-based RDH methods that prioritize either embedding capacity or reconstruction fidelity, the proposed framework seamlessly integrates both objectives within a single lightweight architecture. While the system requires offline construction of two compact codebooks (IC and DC), the runtime pipeline operates without any training or model inference, making it suitable for deployment in edge and IoT environments.

Experimental results across ten standard test images, multiple resolutions (256 × 256, 512 × 512), and varying codebook sizes (64–1024) confirmed consistent PSNR gains of +4 to +5.39 dB and SSIM improvements of +4.12% to +9.86%, with embedding capacities approaching 100 Kbits. Notably, for the Zelda image (512 × 512), SSIM improved from 94.10% to 98.23% while PSNR increased from 37.23 dB to 42.62 dB, achieving near-lossless reconstruction. Compared with existing VQ-based schemes by Wang and Lu (2009) [16], Chang et al. (2021) [41], and Zhao et al. (2014) [2], the proposed RIV + QIC framework consistently outperformed all baselines in both image quality and payload capacity.

The method also demonstrated comparable PSNR gains (up to +3.26 dB) to CNN- and Transformer-based approaches while eliminating their computational overhead and training requirements. The lightweight design ensures practical deployment in resource-constrained IoT and edge devices such as surveillance cameras, mobile healthcare systems, and defense imaging units, without incurring additional bandwidth or computational costs. The unique combination of data hiding and visual enhancement positions this framework as a promising solution for applications demanding both confidentiality and high-fidelity image reconstruction, including medical imaging, national defense, and forensic analysis.

Despite these promising results, several limitations warrant further investigation. First, the current validation focuses primarily on grayscale images at 512 × 512 resolution. While the algorithm’s linear computational complexity O(W×H) enables natural scalability to higher resolutions, extending the framework to color images by processing each RGB channel independently or designing multi-channel codebooks remains an important direction for practical applications such as high-definition medical imaging and multimedia content protection. Second, although the QIC mechanism effectively enhances visual fidelity, the additional memory overhead required to store both the image and difference codebooks warrants quantitative evaluation under different hardware constraints. Third, the current implementation relies on manually tuned Sobel thresholds for edge detection; developing adaptive or learning-based threshold selection mechanisms would improve robustness across diverse image characteristics and dynamic IoT environments. Future work will also focus on extending the approach to video sequences and real-time applications, integrating advanced perceptual metrics beyond PSNR and SSIM, and investigating compatibility with encryption and watermarking frameworks to broaden security capabilities. Furthermore, exploring hybrid integration with lightweight deep neural models—such as combining QIC with pruned CNN or efficient Transformer autoencoders—may further enhance perceptual quality and adaptive embedding while maintaining deployment feasibility on edge devices. A comprehensive comparison with state-of-the-art deep learning methods will also be conducted to systematically evaluate trade-offs between computational complexity, visual fidelity, and embedding capacity across diverse application scenarios.