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Keywords = compressed sensing reconstruction algorithm

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19 pages, 4306 KB  
Article
Sparse Reconstruction of Pressure Field for Wedge Passive Fluidic Thrust Vectoring Nozzle
by Zi Huang, Yunsong Gu, Qiuhui Xu and Linkai Li
Sensors 2026, 26(3), 811; https://doi.org/10.3390/s26030811 - 26 Jan 2026
Abstract
Fluidic thrust vectoring control (FTVC) enables highly agile flight without the mechanical complexity of traditional vectoring nozzles. However, a robust onboard identification of the jet deflection state remains challenging when only limited measurements are available. This study proposes a sparse reconstruction of the [...] Read more.
Fluidic thrust vectoring control (FTVC) enables highly agile flight without the mechanical complexity of traditional vectoring nozzles. However, a robust onboard identification of the jet deflection state remains challenging when only limited measurements are available. This study proposes a sparse reconstruction of the pressure field method for a wedge passive FTVC nozzle and validates the approach experimentally on a low-speed jet platform. By combining the proper orthogonal decomposition (POD) algorithm with an l1-regularized compressed sensing method, a full Coanda wall pressure distribution is reconstructed from the sparse measurements. A genetic algorithm is then employed to optimize the wall pressure tap locations, identifying an optimal layout. With only four pressure taps, the local pressure coefficient errors were maintained within |ΔCp| < 0.02. In contrast, conventional Kriging interpolation requires increasing the sensor count to 13 to approach the reconstruction level of the proposed POD–compressed sensing method using 4 sensors, yet still exhibits a reduced fidelity in capturing key flow structure characteristics. Overall, the proposed approach provides an efficient and physically interpretable strategy for pressure field estimation, supporting lightweight, low-maintenance, and precise fluidic thrust vectoring control. Full article
(This article belongs to the Topic Advanced Engines Technologies)
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23 pages, 2963 KB  
Article
Compressive-Sensing-Based Fast Acquisition Algorithm Using Gram-Matrix Optimization via Direct Projection
by Fangming Zhou, Wang Wang, Yin Xiao and Chen Zhou
Electronics 2026, 15(1), 171; https://doi.org/10.3390/electronics15010171 - 30 Dec 2025
Viewed by 194
Abstract
This paper proposes a compressive-sensing (CS) acquisition algorithm for low-power, high-dynamic GNSS receivers based on low-dimensional time-domain measurements, a non-iterative compressive-domain direct-projection peak-search pipeline, and a coherence-optimized sensing-matrix design. Unlike most existing GNSS-CS acquisition approaches that rely on explicit sparse-recovery formulations (e.g., OMP/BP/LS-type [...] Read more.
This paper proposes a compressive-sensing (CS) acquisition algorithm for low-power, high-dynamic GNSS receivers based on low-dimensional time-domain measurements, a non-iterative compressive-domain direct-projection peak-search pipeline, and a coherence-optimized sensing-matrix design. Unlike most existing GNSS-CS acquisition approaches that rely on explicit sparse-recovery formulations (e.g., OMP/BP/LS-type iterative reconstruction) to identify the delay–Doppler support—often incurring substantial computational burden and acquisition latency—the proposed method performs peak detection directly in the compressive measurement domain and is supported by unified Gram-matrix optimization and perturbation/detection analyses. Specifically, the measurement Gram matrix is optimized on the symmetric positive-definite (SPD) manifold to obtain a diagonally dominant and well-conditioned structure with reduced inter-column correlation, thereby bounding reconstruction-induced perturbations and preserving the main correlation peak. Simulation results show that the proposed scheme retains the low online complexity characteristic of direct-projection baselines while achieving a 2–3 dB acquisition sensitivity gain, and it requires substantially fewer operations than iterative OMP-based CS acquisition schemes whose cost scales approximately linearly with the sparsity level K. The proposed framework enables robust, low-latency acquisition suitable for resource-constrained GNSS receivers in high-dynamic environments. Full article
(This article belongs to the Section Microwave and Wireless Communications)
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20 pages, 1176 KB  
Article
DnCNN-Based Denoising Model for Low-Dose Myocardial CT Perfusion Imaging
by Mahmud Hasan, Aaron So and Mahmoud R. El-Sakka
Electronics 2026, 15(1), 124; https://doi.org/10.3390/electronics15010124 - 26 Dec 2025
Cited by 1 | Viewed by 244
Abstract
Unlike high-dose scans, low-dose cardiac CT perfusion imaging reduces patient radiation exposure and thereby the risk of potential health effects. However, it introduces significant image noise, degrading diagnostic quality and limiting clinical assessment. Denoising is thus a critical preprocessing step to enhance image [...] Read more.
Unlike high-dose scans, low-dose cardiac CT perfusion imaging reduces patient radiation exposure and thereby the risk of potential health effects. However, it introduces significant image noise, degrading diagnostic quality and limiting clinical assessment. Denoising is thus a critical preprocessing step to enhance image quality without compromising anatomical or perfusion details. Traditionally used reconstruction-domain methods, such as Iterative Reconstruction and Compressed Sensing, are often limited by algorithmic complexity, dependence on raw sinogram data, and restricted adaptability. Conversely, image-domain methods offer more adaptable denoising options. Recently, learning-based approaches have further expanded this flexibility and demonstrated state-of-the-art performance across various denoising tasks. In this work, we present a deep learning-based denoising method specifically tuned for low-dose cardiac CT perfusion imaging. Our model is trained to reduce noise while preserving structural integrity and temporal contrast dynamics, which are critical for downstream analysis. Unlike many existing methods, our approach is optimized for perfusion data, where temporal consistency is essential. Residual cardiac motion remains a separate challenge, which we aim to address in our future work. Experimental results show significant improvements in quantitative image quality, using both reference-based and no-reference metrics, such as MSE/PSNR/SSIM and NIQE/FID/KID, as well as improved accuracy of perfusion measurements. Full article
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30 pages, 6264 KB  
Article
An Efficient Image Encryption Scheme Based on DNA Mutations and Compression Sensing
by Jianhua Qiu, Shenli Zhu, Yu Liu, Xize Luo, Dongxin Liu, Hui Zhou, Congxu Zhu and Zheng Qin
Mathematics 2026, 14(1), 5; https://doi.org/10.3390/math14010005 - 19 Dec 2025
Viewed by 291
Abstract
In communication environments with limited computing resources, securely and efficiently transmitting image data has become a challenging problem. However, most existing image data protection schemes are based on high-dimensional chaotic systems as key generators, which suffer from issues such as high algorithmic complexity [...] Read more.
In communication environments with limited computing resources, securely and efficiently transmitting image data has become a challenging problem. However, most existing image data protection schemes are based on high-dimensional chaotic systems as key generators, which suffer from issues such as high algorithmic complexity and large computational overhead. To address this, this paper presents new designs for a 1D Sine Fractional Chaotic Map (1D-SFCM) as a random sequence generator and provides mathematical proofs related to the boundedness and fixed points of this model. Furthermore, this paper improves the traditional 2D compressive sensing (2DCS) algorithm by using the newly designed 1D-SFCM map to generate a chaotic measurement matrix, which can effectively enhance the quality of image recovery and reconstruction. Moreover, referring to the principle of gene mutation in biogenetics, this paper designs an image encryption algorithm based on DNA base substitution. Finally, the security of the proposed encryption scheme and the quality of image compression and reconstruction are verified through indicators such as key space, information entropy, and Number of Pixel Change Rate (NPCR). Full article
(This article belongs to the Special Issue Chaotic Systems and Their Applications, 2nd Edition)
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21 pages, 4212 KB  
Article
A Low-Cost Detection Method for Acoustic Defects in Building Components: Compressed Nearfield Acoustic Holography
by Chenxi Yang, Hongwei Wang, Qiaochu Wang and Shujie Li
Acoustics 2025, 7(4), 69; https://doi.org/10.3390/acoustics7040069 - 30 Oct 2025
Viewed by 701
Abstract
The accurate diagnosis of acoustic defects and the precise assessment of the performance of building components are highly dependent on massive amounts of sampling data. In this study, we try to combine the compressed sensing theory with the nearfield acoustic holographic sound insulation [...] Read more.
The accurate diagnosis of acoustic defects and the precise assessment of the performance of building components are highly dependent on massive amounts of sampling data. In this study, we try to combine the compressed sensing theory with the nearfield acoustic holographic sound insulation measurement method and introduce a noise reduction algorithm so as to realize the sound pressure distribution accuracy similar to that of the conventional sampling under low-density data conditions. Numerical simulation results show that the reconstruction error of the method proposed in this paper is only 8.21% higher than that of the complete sampling under the condition of 20% sampling rate, and the reconstruction error is only 2.50% higher than that of the complete sampling under the condition of 40% sampling rate. The reconstruction error under 50% sampling rate and 6.65 dB SNR is only 4.81% higher than the complete sampling, which is basically consistent with the numerical simulation; the sound insulation is only 1 dB lower than that measured by the sound pressure method, and the acoustic defects of the components can basically be identified. The results of this study have a positive significance in simplifying the process of sound insulation measurement in most scenarios. Full article
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21 pages, 3949 KB  
Article
Non-Iterative Shrinkage-Thresholding-Reconstructed Compressive Acquisition Algorithm for High-Dynamic GNSS Signals
by Zhuang Ma, Mingliang Deng, Hui Huang, Xiaohong Wang and Qiang Liu
Aerospace 2025, 12(11), 958; https://doi.org/10.3390/aerospace12110958 - 27 Oct 2025
Cited by 1 | Viewed by 527
Abstract
Owing to the intrinsic sparsity of GNSS signals in the correlation domain, compressed sensing (CS) is attractive for the rapid acquisition of high-dynamic GNSS signals. However, the compressed measurement-associated noise folding inherently amplifies the pre-measurement noise, leading to an inevitable degradation of acquisition [...] Read more.
Owing to the intrinsic sparsity of GNSS signals in the correlation domain, compressed sensing (CS) is attractive for the rapid acquisition of high-dynamic GNSS signals. However, the compressed measurement-associated noise folding inherently amplifies the pre-measurement noise, leading to an inevitable degradation of acquisition performance. In this paper, a novel CS-based GNSS signal acquisition algorithm is, for the first time, proposed with the efficient suppression of the amplified measurement noise and low computational complexities. The offline developed code phase and frequency bin-compressed matrices in the correlation domain are utilized to obtain a real-time observed matrix, from which the correlation matrix of the GNSS signal is rapidly reconstructed via a denoised back-projection and a non-iterative shrinkage-thresholding (NIST) operation. A detailed theoretical analysis and extensive numerical explorations are undertaken for the algorithm computational complexity, the achievable acquisition performance, and the algorithm performance robustness to various Doppler frequencies. It is shown that, compared with the classic orthogonal matching pursuit (OMP) reconstruction, the NIST reconstruction gives rise to a 3.3 dB improvement in detection sensitivity with a computational complexity increase of <10%. Moreover, the NIST-reconstructed CS acquisition algorithm outperforms the conventional CS acquisition algorithm with frequency serial search (FSS) in terms of both the acquisition performance and the computational complexity. In addition, a variation in the detection sensitivity is observed as low as 1.3 dB over a Doppler frequency range from 100 kHz to 200 kHz. Full article
(This article belongs to the Section Astronautics & Space Science)
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20 pages, 3102 KB  
Article
Compressive Sensing-Based 3D Spectrum Extrapolation for IoT Coverage in Obstructed Urban Areas
by Kun Yin, Shengliang Fang and Feihuang Chu
Electronics 2025, 14(21), 4177; https://doi.org/10.3390/electronics14214177 - 26 Oct 2025
Viewed by 424
Abstract
As a fundamental information carrier in Industrial Internet of Things (IIoT), electromagnetic spectrum data presents critical challenges for efficient spectrum sensing and situational awareness in smart industrial cognitive radio systems. Addressing sparse sampling limitations caused by energy-constrained transceiver nodes in Unmanned Aerial Vehicle [...] Read more.
As a fundamental information carrier in Industrial Internet of Things (IIoT), electromagnetic spectrum data presents critical challenges for efficient spectrum sensing and situational awareness in smart industrial cognitive radio systems. Addressing sparse sampling limitations caused by energy-constrained transceiver nodes in Unmanned Aerial Vehicle (UAV) spectrum monitoring, this paper proposes a compressive sensing-based 3D spectrum tensor completion framework for extrapolative reconstruction in obstructed areas (e.g., building occlusions). First, a Sparse Coding Neural Gas (SCNG) algorithm constructs an overcomplete dictionary adaptive to wide-range spectral fluctuations. Subsequently, a Bag of Pursuits-optimized Orthogonal Matching Pursuit (BoP-OOMP) framework enables adaptive key-point sampling through multi-path tree search and temporary orthogonal matrix dimensionality reduction. Finally, a Neural Gas competitive learning strategy leverages intermediate BoP solutions for gradient-weighted dictionary updates, eliminating computational redundancy. Benchmark results demonstrate 43.2% reconstruction error reduction at sampling ratios r ≤ 20% across full-space measurements, while achieving decoupling of highly correlated overlapping subspaces—validating superior estimation accuracy and computational efficiency. Full article
(This article belongs to the Special Issue Advances in Cognitive Radio and Cognitive Radio Networks)
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21 pages, 4796 KB  
Article
Deep Bayesian Optimization of Sparse Aperture for Compressed Sensing 3D ISAR Imaging
by Zongkai Yang, Jingcheng Zhao, Mengyu Zhang, Changyu Lou and Xin Zhao
Remote Sens. 2025, 17(19), 3380; https://doi.org/10.3390/rs17193380 - 7 Oct 2025
Viewed by 803
Abstract
High-resolution three-dimensional (3D) Inverse Synthetic Aperture Radar (ISAR) imaging is essential for the characterization of target scattering in various environments. The practical application of this technique is frequently impeded by the lengthy measurement time necessary for comprehensive data acquisition with turntable-based systems. Sub-sampling [...] Read more.
High-resolution three-dimensional (3D) Inverse Synthetic Aperture Radar (ISAR) imaging is essential for the characterization of target scattering in various environments. The practical application of this technique is frequently impeded by the lengthy measurement time necessary for comprehensive data acquisition with turntable-based systems. Sub-sampling the aperture can decrease acquisition time; however, traditional reconstruction algorithms that utilize matched filtering exhibit significantly impaired imaging performance, often characterized by a high peak side-lobe ratio. A methodology is proposed that integrates compressed sensing(CS) theory with sparse-aperture optimization to achieve high-fidelity 3D imaging from sparsely sampled data. An optimized sparse sampling aperture is introduced to systematically balance the engineering requirement for efficient, continuous turntable motion with the low mutual coherence desired for the CS matrix. A deep Bayesian optimization framework was developed to automatically identify physically realizable optimal sampling trajectories, ensuring that the sensing matrix retains the necessary properties for accurate signal recovery. This method effectively addresses the high-sidelobe problem associated with traditional sparse techniques, significantly decreasing measurement duration while maintaining image quality. Quantitative experimental results indicate the method’s efficacy: the optimized sparse aperture decreases the number of angular sampling points by roughly 84% compared to a full acquisition, while reconstructing images with a high correlation coefficient of 0.98 to the fully sampled reference. The methodology provides an effective solution for rapid, high-performance 3D ISAR imaging, achieving an optimal balance between data acquisition efficiency and reconstruction fidelity. Full article
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21 pages, 741 KB  
Article
A DH-KSVD Algorithm for Efficient Compression of Shock Wave Data
by Jiarong Liu, Yonghong Ding and Wenbin You
Appl. Sci. 2025, 15(19), 10640; https://doi.org/10.3390/app151910640 - 1 Oct 2025
Viewed by 558
Abstract
To address low training efficiency and poor reconstruction in traditional K Singular Value Decomposition (KSVD) for compressive sensing of shock wave signals, this study proposes an improved algorithm, DH-KSVD, integrating dynamic pruning and hybrid coding. The dynamic pruning mechanism eliminates redundant atoms according [...] Read more.
To address low training efficiency and poor reconstruction in traditional K Singular Value Decomposition (KSVD) for compressive sensing of shock wave signals, this study proposes an improved algorithm, DH-KSVD, integrating dynamic pruning and hybrid coding. The dynamic pruning mechanism eliminates redundant atoms according to their contributions and adaptive thresholds, while incorporating residual features to enhance dictionary compactness and training efficiency. The hybrid sparse constraint integrates the sparsity of 0-Orthogonal Matching Pursuit (OMP) with the noise robustness of 1-Least Absolute Shrinkage and Selection Operator (LASSO), dynamically adjusting their relative weights to enhance both coding quality and reconstruction stability. Experiments on typical shock wave datasets show that, compared with Discrete Cosine Transform (DCT), KSVD, and feature-based segmented dictionary methods (termed CC-KSVD), DH-KSVD reduces average training time by 46.4%, 31%, and 13.7%, respectively. At a Compression Ratio (CR) of 0.7, the Root Mean Square Error (RMSE) decreases by 67.1%, 65.7%, and 36.2%, while the Peak Signal-to-Noise Ratio (PSNR) increases by 35.5%, 39.8%, and 11.8%, respectively. The proposed algorithm markedly improves training efficiency and achieves lower RMSE and higher PSNR under high compression ratios, providing an effective solution for compressing long-duration, transient shock wave signals. Full article
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15 pages, 356 KB  
Article
Computing One-Bit Compressive Sensing via Alternating Proximal Algorithm
by Jin-Jiang Wang and Yan-Hong Hu
Mathematics 2025, 13(18), 2926; https://doi.org/10.3390/math13182926 - 10 Sep 2025
Viewed by 558
Abstract
It is challenging to recover a real sparse signal using one-bit compressive sensing. Existing methods work well when there is no noise (sign flips) in the measurements or the noise level or a priori information about signal sparsity is known. However, the noise [...] Read more.
It is challenging to recover a real sparse signal using one-bit compressive sensing. Existing methods work well when there is no noise (sign flips) in the measurements or the noise level or a priori information about signal sparsity is known. However, the noise level and a priori information about signal sparsity are not always known in practice. In this paper, we propose a robust model with a non-smooth and non-convex objective function. In this model, the noise factor is considered without knowing the noise level or a priori information about the signal sparsity. We develop an alternating proximal algorithm and prove that the sequence generated from the algorithm converges to a local minimizer of the model. Our algrithm possesses high time efficiency and recovery accuracy. It performs better than other algorithms tested in our experiments when the the noise level and the sparsity of the signal is known. Full article
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19 pages, 5242 KB  
Article
Single-Pixel Three-Dimensional Compressive Imaging System Using Volume Structured Illumination
by Yanbing Jiang and Shaoshuo Mu
Electronics 2025, 14(17), 3463; https://doi.org/10.3390/electronics14173463 - 29 Aug 2025
Viewed by 1013
Abstract
Single-pixel imaging enables two-dimensional image capture through a single-pixel detector, yet extending this to three-dimensional or higher-dimensional information capture in single-pixel optical imaging systems has remained a challenging problem. In this study, we present a single-pixel camera system for three-dimensional (3D) imaging based [...] Read more.
Single-pixel imaging enables two-dimensional image capture through a single-pixel detector, yet extending this to three-dimensional or higher-dimensional information capture in single-pixel optical imaging systems has remained a challenging problem. In this study, we present a single-pixel camera system for three-dimensional (3D) imaging based on compressed sensing (CS) with continuous wave (CW) pseudo-random volume structured illumination. An estimated image, which incorporates both spatial and depth information of a 3D scene, is reconstructed using an L1-norm minimization reconstruction algorithm. This algorithm employs prior knowledge of non-overlapping objects as a constraint in the target space, resulting in improved noise performance in both numerical simulations and physical experiments. Our simulations and experiments demonstrate the feasibility of the proposed 3D CS framework. This approach achieves compressive sensing in a 3D information capture system with a measurement ratio of 19.53%. Additionally, we show that our CS 3D capturing system can accurately reconstruct the color of a target using color filter modulation. Full article
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23 pages, 6848 KB  
Review
The Expanding Frontier: The Role of Artificial Intelligence in Pediatric Neuroradiology
by Alessia Guarnera, Antonio Napolitano, Flavia Liporace, Fabio Marconi, Maria Camilla Rossi-Espagnet, Carlo Gandolfo, Andrea Romano, Alessandro Bozzao and Daniela Longo
Children 2025, 12(9), 1127; https://doi.org/10.3390/children12091127 - 27 Aug 2025
Viewed by 1812
Abstract
Artificial intelligence (AI) is revolutionarily shaping the entire landscape of medicine and particularly the privileged field of radiology, since it produces a significant amount of data, namely, images. Currently, AI implementation in radiology is continuously increasing, from automating image analysis to enhancing workflow [...] Read more.
Artificial intelligence (AI) is revolutionarily shaping the entire landscape of medicine and particularly the privileged field of radiology, since it produces a significant amount of data, namely, images. Currently, AI implementation in radiology is continuously increasing, from automating image analysis to enhancing workflow management, and specifically, pediatric neuroradiology is emerging as an expanding frontier. Pediatric neuroradiology presents unique opportunities and challenges since neonates’ and small children’s brains are continuously developing, with age-specific changes in terms of anatomy, physiology, and disease presentation. By enhancing diagnostic accuracy, reducing reporting times, and enabling earlier intervention, AI has the potential to significantly impact clinical practice and patients’ quality of life and outcomes. For instance, AI reduces MRI and CT scanner time by employing advanced deep learning (DL) algorithms to accelerate image acquisition through compressed sensing and undersampling, and to enhance image reconstruction by denoising and super-resolving low-quality datasets, thereby producing diagnostic-quality images with significantly fewer data points and in a shorter timeframe. Furthermore, as healthcare systems become increasingly burdened by rising demands and limited radiology workforce capacity, AI offers a practical solution to support clinical decision-making, particularly in institutions where pediatric neuroradiology is limited. For example, the MELD (Multicenter Epilepsy Lesion Detection) algorithm is specifically designed to help radiologists find focal cortical dysplasias (FCDs), which are a common cause of drug-resistant epilepsy. It works by analyzing a patient’s MRI scan and comparing a wide range of features—such as cortical thickness and folding patterns—to a large database of scans from both healthy individuals and epilepsy patients. By identifying subtle deviations from normal brain anatomy, the MELD graph algorithm can highlight potential lesions that are often missed by the human eye, which is a critical step in identifying patients who could benefit from life-changing epilepsy surgery. On the other hand, the integration of AI into pediatric neuroradiology faces technical and ethical challenges, such as data scarcity and ethical and legal restrictions on pediatric data sharing, that complicate the development of robust and generalizable AI models. Moreover, many radiologists remain sceptical of AI’s interpretability and reliability, and there are also important medico-legal questions around responsibility and liability when AI systems are involved in clinical decision-making. Future promising perspectives to overcome these concerns are represented by federated learning and collaborative research and AI development, which require technological innovation and multidisciplinary collaboration between neuroradiologists, data scientists, ethicists, and pediatricians. The paper aims to address: (1) current applications of AI in pediatric neuroradiology; (2) current challenges and ethical considerations related to AI implementation in pediatric neuroradiology; and (3) future opportunities in the clinical and educational pediatric neuroradiology field. AI in pediatric neuroradiology is not meant to replace neuroradiologists, but to amplify human intellect and extend our capacity to diagnose, prognosticate, and treat with unprecedented precision and speed. Full article
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21 pages, 4917 KB  
Article
A High-Capacity Reversible Data Hiding Scheme for Encrypted Hyperspectral Images Using Multi-Layer MSB Block Labeling and ERLE Compression
by Yijie Lin, Chia-Chen Lin, Zhe-Min Yeh, Ching-Chun Chang and Chin-Chen Chang
Future Internet 2025, 17(8), 378; https://doi.org/10.3390/fi17080378 - 21 Aug 2025
Cited by 1 | Viewed by 721
Abstract
In the context of secure and efficient data transmission over the future Internet, particularly for remote sensing and geospatial applications, reversible data hiding (RDH) in encrypted hyperspectral images (HSIs) has emerged as a critical technology. This paper proposes a novel RDH scheme specifically [...] Read more.
In the context of secure and efficient data transmission over the future Internet, particularly for remote sensing and geospatial applications, reversible data hiding (RDH) in encrypted hyperspectral images (HSIs) has emerged as a critical technology. This paper proposes a novel RDH scheme specifically designed for encrypted HSIs, offering enhanced embedding capacity without compromising data security or reversibility. The approach introduces a multi-layer block labeling mechanism that leverages the similarity of most significant bits (MSBs) to accurately locate embeddable regions. To minimize auxiliary information overhead, we incorporate an Extended Run-Length Encoding (ERLE) algorithm for effective label map compression. The proposed method achieves embedding rates of up to 3.79 bits per pixel per band (bpppb), while ensuring high-fidelity reconstruction, as validated by strong PSNR metrics. Comprehensive security evaluations using NPCR, UACI, and entropy confirm the robustness of the encryption. Extensive experiments across six standard hyperspectral datasets demonstrate the superiority of our method over existing RDH techniques in terms of capacity, embedding rate, and reconstruction quality. These results underline the method’s potential for secure data embedding in next-generation Internet-based geospatial and remote sensing systems. Full article
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25 pages, 6031 KB  
Article
Sparse Transform and Compressed Sensing Methods to Improve Efficiency and Quality in Magnetic Resonance Medical Imaging
by Santiago Villota and Esteban Inga
Sensors 2025, 25(16), 5137; https://doi.org/10.3390/s25165137 - 19 Aug 2025
Viewed by 2267
Abstract
This paper explores the application of transform-domain sparsification and compressed sensing (CS) techniques to improve the efficiency and quality of magnetic resonance imaging (MRI). We implement and evaluate three sparsifying methods—discrete wavelet transform (DWT), fast Fourier transform (FFT), and discrete cosine transform (DCT)—which [...] Read more.
This paper explores the application of transform-domain sparsification and compressed sensing (CS) techniques to improve the efficiency and quality of magnetic resonance imaging (MRI). We implement and evaluate three sparsifying methods—discrete wavelet transform (DWT), fast Fourier transform (FFT), and discrete cosine transform (DCT)—which are used to simulate subsampled reconstruction via inverse transforms. Additionally, one accurate CS reconstruction algorithm, basis pursuit (BP), using the L1-MAGIC toolbox, is implemented as a benchmark based on convex optimization with L1-norm minimization. Emphasis is placed on basis pursuit (BP), which satisfies the formal requirements of CS theory, including incoherent sampling and sparse recovery via nonlinear reconstruction. Each method is assessed in MATLAB R2024b using standardized DICOM images and varying sampling rates. The evaluation metrics include peak signal-to-noise ratio (PSNR), root mean square error (RMSE), structural similarity index measure (SSIM), execution time, memory usage, and compression efficiency. The results show that although discrete cosine transform (DCT) outperforms the others under simulation in terms of PSNR and SSIM, it is inconsistent with the physics of MRI acquisition. Conversely, basis pursuit (BP) offers a theoretically grounded reconstruction approach with acceptable accuracy and clinical relevance. Despite the limitations of a controlled experimental setup, this study establishes a reproducible benchmarking framework and highlights the trade-offs between the quality of transform-based reconstruction and computational complexity. Future work will extend this study by incorporating clinically validated CS algorithms with L0 and nonconvex Lp (0 < p < 1) regularization to align with state-of-the-art MRI reconstruction practices. Full article
(This article belongs to the Section Industrial Sensors)
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17 pages, 2693 KB  
Article
Mitigating the Drawbacks of the L0 Norm and the Total Variation Norm
by Gengsheng L. Zeng
Axioms 2025, 14(8), 605; https://doi.org/10.3390/axioms14080605 - 4 Aug 2025
Viewed by 954
Abstract
In compressed sensing, it is believed that the L0 norm minimization is the best way to enforce a sparse solution. However, the L0 norm is difficult to implement in a gradient-based iterative image reconstruction algorithm. The total variation (TV) norm minimization [...] Read more.
In compressed sensing, it is believed that the L0 norm minimization is the best way to enforce a sparse solution. However, the L0 norm is difficult to implement in a gradient-based iterative image reconstruction algorithm. The total variation (TV) norm minimization is considered a proper substitute for the L0 norm minimization. This paper points out that the TV norm is not powerful enough to enforce a piecewise-constant image. This paper uses the limited-angle tomography to illustrate the possibility of using the L0 norm to encourage a piecewise-constant image. However, one of the drawbacks of the L0 norm is that its derivative is zero almost everywhere, making a gradient-based algorithm useless. Our novel idea is to replace the zero value of the L0 norm derivative with a zero-mean random variable. Computer simulations show that the proposed L0 norm minimization outperforms the TV minimization. The novelty of this paper is the introduction of some randomness in the gradient of the objective function when the gradient is zero. The quantitative evaluations indicate the improvements of the proposed method in terms of the structural similarity (SSIM) and the peak signal-to-noise ratio (PSNR). Full article
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