A Novel High-Fidelity Reversible Data Hiding Method Based on Adaptive Multi-pass Embedding
Abstract
:1. Introduction
2. Related Work
2.1. Single-Pass PVO-Based Reversible Data Hiding
2.2. Multi-Pass PVO-Based Reversible Data Hiding
2.3. Pairwise PVO-Based Reversible Data Hiding
3. Proposed Method
3.1. Adaptive k-Pass PVO-Based Prediction
- If , the embedded data are extracted as as and as and the pixel value is restored as .
- (a)
- If or , there is neither data extraction nor pixel restoration.
- (b)
- If , the embedded data are extracted as and the pixel value is restored as .
- (c)
- If , the embedded bit is extracted as and the pixel value is restored as .
- If , there is no data extraction and the pixel value is restored as .
- (a)
- If , the embedded bit is extracted as and the pixel value is restored as .
- (b)
- If , the embedded bit is extracted as and the pixel value is restored as .
3.2. Content-Based IPVO-Based Pairwise PEE
3.3. Content-Based Adaptive k
3.4. Implementation of the Proposed Method
- The length of binary auxiliary information (10 bits).
- Block size (4 bits).
- Thresholds ( bits).
- Parameter k ( bits).
- Embedding capacity (16 bits).
- Length of the compressed location map (16 bits).
- Auxiliary information extraction The LSBs of the first two lines pixels of the marked image are read to retrieve auxiliary information. First, the length of the binary auxiliary information is obtained according to the first 10 bits of the extracted data. Following, the auxiliary information is extracted.
- Data extraction and image restoration The marked image is divided into non-overlapped blocks with the extracted block size. The noise level of pixel block is calculated. If , extraction is performed with the help of the extracted parameter k and . Otherwise, the block is skipped.
- Restoration of the rest pixels The first two lines of bits data of are used to recover the first two lines of pixels. Then, the location map is restored by decompressing the compressed location map. Finally, pixels valued 0 or 255 are restored according to the location map.
4. Experimental Results
4.1. Analysis of Three Proposed Methods
4.2. Analysis of Parameters
4.3. Comparison with Advanced Methods
4.4. t-Test
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Symbol | Description | Symbol | Description |
---|---|---|---|
Pixel value at position in the sorted sequence | Mapping function that maps sorted index i to original pixel position | ||
Size of non-overlapped blocks | n | Total number of pixels in a block | |
Prediction error for the largest pixel | Prediction error for the smallest pixel | ||
Prediction error for pixel at position | Prediction error for pixel at position | ||
, , | Modified prediction errors after data embedding | Modified pixel value after data embedding | |
Pixel value at position i in the unsorted sequence | , | Binary secret data bits (0 or 1) to be embedded | |
L | Index in range | S | Index in range |
k | Parameter controlling number of pixels processed in each pass | The number of classes for pixel blocks based on noise level NL | |
Ideal k in a pixel block | Embedding parameter for noise level | ||
The collection of noise level thresholds for pixel blocks | Optimal thresholds collection for noise level classification |
EC = 10,000 | EC = 20,000 | EC = 30,000 | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
PSNR | PSNR | PSNR | ||||||||||
KP-IPVO | (20,26,57) | 61.47 | (25,31,43,82) | 57.66 | (35,51,119) | 54.90 | ||||||
PairwiseKP-IPVO | (4,6,44,44,49) | 61.49 | (3,46,51) | 57.86 | (4,4,82) | 55.32 |
[25] | [26] | [35] | [32] | [36] | [39] | Proposed | |
---|---|---|---|---|---|---|---|
Lena | 58.99 | 59.16 | 61.08 | 60.81 | 61.02 | 61.01 | 61.56 |
Airplane | 62.89 | 63.05 | 63.86 | 63.50 | 63.70 | 63.70 | 64.24 |
Baboon | 53.58 | 54.15 | 54.63 | 54.92 | 55.13 | 55.13 | 55.18 |
Barbara | 60.47 | 60.45 | 61.08 | 61.11 | 61.08 | 60.96 | 61.22 |
Boat | 58.88 | 59.23 | 60.51 | 58.73 | 58.83 | 58.78 | 59.23 |
Elaine | 57.35 | 57.36 | 59.14 | 57.81 | 58.56 | 58.75 | 59.28 |
Lake | 58.26 | 58.06 | 58.85 | 59.70 | 60.03 | 60.43 | 60.99 |
Peppers | 60.46 | 60.57 | 60.77 | 59.54 | 59.24 | 59.61 | 59.86 |
Average | 58.86 | 59.00 | 59.99 | 59.51 | 59.70 | 59.80 | 60.19 |
[25] | [26] | [35] | [32] | [36] | [39] | Proposed | |
---|---|---|---|---|---|---|---|
Lena | 56.53 | 56.60 | 57.30 | 57.14 | 57.18 | 57.34 | 57.87 |
Airplane | 59.06 | 59.26 | 60.34 | 59.72 | 59.97 | 59.97 | 60.94 |
Baboon | - | - | - | - | - | - | - |
Barbara | 56.18 | 56.50 | 56.92 | 57.04 | 57.10 | 57.09 | 57.51 |
Boat | 53.85 | 53.72 | 54.40 | 54.53 | 54.63 | 54.51 | 54.88 |
Elaine | 52.60 | 52.71 | 53.87 | 53.62 | 53.85 | 53.87 | 54.19 |
Lake | 53.63 | 54.28 | 55.34 | 54.92 | 54.96 | 55.41 | 55.73 |
Peppers | 54.78 | 54.93 | 55.37 | 55.58 | 55.24 | 55.67 | 55.76 |
Average | 55.23 | 55.43 | 56.22 | 56.08 | 56.13 | 56.27 | 56.70 |
Image | PSNR (dB) | MSE | ||||||||
---|---|---|---|---|---|---|---|---|---|---|
Proposed | [26] | [24] | [25] | [39] | Proposed | [26] | [24] | [25] | [39] | |
kodim01 | 62.68 | 62.36 | 50.25 | 60.43 | 63.64 | 0.035 | 0.038 | 0.613 | 0.059 | 0.028 |
kodim02 | 62.81 | 62.78 | 52.31 | 61.06 | 64.23 | 0.034 | 0.034 | 0.382 | 0.051 | 0.025 |
kodim03 | 63.93 | 63.74 | 49.55 | 59.15 | 65.04 | 0.026 | 0.028 | 0.720 | 0.079 | 0.020 |
kodim04 | 62.76 | 62.75 | 52.74 | 61.59 | 63.79 | 0.034 | 0.034 | 0.346 | 0.045 | 0.027 |
kodim05 | 61.70 | 61.31 | - | 53.25 | 63.38 | 0.044 | 0.048 | - | 0.307 | 0.030 |
kodim06 | 64.95 | 64.47 | - | - | 66.70 | 0.021 | 0.023 | - | - | 0.014 |
kodim07 | 63.60 | 63.39 | 53.25 | 62.59 | 64.42 | 0.028 | 0.030 | 0.307 | 0.036 | 0.024 |
kodim08 | 60.03 | 56.79 | - | - | 57.04 | 0.065 | 0.136 | - | - | 0.128 |
kodim09 | 62.17 | 62.11 | 53.62 | 62.09 | 61.73 | 0.039 | 0.040 | 0.283 | 0.040 | 0.044 |
kodim10 | 62.29 | 61.44 | 48.58 | 57.17 | 60.98 | 0.038 | 0.047 | 0.901 | 0.125 | 0.052 |
kodim11 | 63.85 | 63.65 | 52.95 | 62.74 | 64.83 | 0.027 | 0.028 | 0.330 | 0.035 | 0.021 |
kodim12 | 63.36 | 63.43 | - | 54.81 | 64.45 | 0.030 | 0.030 | - | 0.215 | 0.023 |
kodim13 | 59.86 | 56.93 | - | - | 58.46 | 0.067 | 0.132 | - | - | 0.093 |
kodim14 | 61.27 | 61.23 | 48.72 | 57.57 | 62.83 | 0.048 | 0.049 | 0.874 | 0.114 | 0.034 |
kodim15 | 64.27 | 61.62 | - | - | 61.10 | 0.024 | 0.045 | - | - | 0.050 |
kodim16 | 63.68 | 63.56 | 52.39 | 61.67 | 64.81 | 0.028 | 0.029 | 0.375 | 0.044 | 0.021 |
kodim17 | 62.87 | 62.66 | 54.81 | 63.57 | 62.91 | 0.033 | 0.035 | 0.215 | 0.029 | 0.033 |
kodim18 | 60.09 | 59.42 | 46.54 | 54.39 | 59.36 | 0.064 | 0.074 | 1.443 | 0.236 | 0.075 |
kodim19 | 61.90 | 61.78 | 51.60 | 59.94 | 62.03 | 0.042 | 0.043 | 0.450 | 0.066 | 0.041 |
kodim20 | 62.31 | 53.76 | - | - | 52.26 | 0.038 | 0.274 | - | - | 0.387 |
kodim21 | 62.37 | 62.03 | 46.68 | 55.38 | 61.78 | 0.038 | 0.041 | 1.402 | 0.188 | 0.043 |
kodim22 | 61.78 | 61.54 | - | 53.55 | 61.43 | 0.043 | 0.046 | - | 0.288 | 0.047 |
kodim23 | 63.51 | 62.83 | 46.99 | 55.98 | 63.16 | 0.029 | 0.034 | 1.301 | 0.164 | 0.031 |
kodim24 | 63.10 | 58.67 | - | - | 56.93 | 0.032 | 0.088 | - | - | 0.132 |
Average | 62.55 | 61.43 | 50.73 | 58.72 | 61.97 | 0.036 | 0.049 | 0.550 | 0.089 | 0.041 |
[24] | [36] | [39] | [32] | |
---|---|---|---|---|
Lena | 28.72 | 8.01 | 10.84 | 39.37 |
Barbara | 10.00 | 3.02 | 14.49 | 5.44 |
Boat | 53.53 | 5.48 | 7.79 | 16.34 |
Elaine | 15.59 | 3.35 | 5.83 | 6.74 |
Lake | 46.43 | 7.42 | 10.32 | 18.53 |
Peppers | 25.70 | −6.25 | 1.32 | 9.52 |
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Kong, X.; He, W.; Cai, Z. A Novel High-Fidelity Reversible Data Hiding Method Based on Adaptive Multi-pass Embedding. Mathematics 2025, 13, 1881. https://doi.org/10.3390/math13111881
Kong X, He W, Cai Z. A Novel High-Fidelity Reversible Data Hiding Method Based on Adaptive Multi-pass Embedding. Mathematics. 2025; 13(11):1881. https://doi.org/10.3390/math13111881
Chicago/Turabian StyleKong, Xiaoxi, Wenguang He, and Zhanchuan Cai. 2025. "A Novel High-Fidelity Reversible Data Hiding Method Based on Adaptive Multi-pass Embedding" Mathematics 13, no. 11: 1881. https://doi.org/10.3390/math13111881
APA StyleKong, X., He, W., & Cai, Z. (2025). A Novel High-Fidelity Reversible Data Hiding Method Based on Adaptive Multi-pass Embedding. Mathematics, 13(11), 1881. https://doi.org/10.3390/math13111881