Compressive Sensing Research Articles

NL-CS Net: Deep Learning with Non-local Prior for Image Compressive Sensing

NL-CS Net: Deep Learning with Non-local Prior for Image Compressive Sensing

Volatility-based diversity awareness for distributed data storage of Mobile Crowd Sensing

With the widespread utilization of sensors and the rapid development of Mobile Crowd Sensing (MCS), the framework of distributed data storage, which makes use of the limited storage capacity of sensing devices, is providing an alternative to cloud-based data storage. Since the construction of the distributed storage framework for MCS has to be completed by Compressed Sensing (CS) theory, a reasonable measurement allocation becomes a no-brainer if we want to obtain more recovery precision of data without wasting measurement resources. To more efficiently address the above problems, we present a novel strategy of Volatility-Based Diversity Awareness for CS measurement allocation called VBDA, which collectively achieves lower computational complexity, adaptive sampling rate allocation for non-visual data, and high-quality reconstruction. We first process the target monitoring region in blocks. Then, we calculate the degree of data diversity of each area using the volatility, which is used to assess the importance of the different areas. Worthy note, based on the volatility calculation, we can obtain the magnitude of the variation in diversity that is only present in the real data, even when using very ambiguous recovered data. This is primarily due to the volatility unique design concept, which attempts to offset partially identical errors in adjacent recovered data using volatility calculations. Finally, to rationally allocate measurement resources, a volatility-based sampling rate allocation scheme is proposed. We further provide an implementation for practical deployments of VBDA in various related contexts. Numerous experimental show that the VBDA performs excellently. In comparison to the current state-of-the-art strategy, it improves data recovery accuracy by 12.2% without the use of any prior knowledge, while being adaptable to many different distribution types of data.

Group sparsity residual constraint model with weighted log-sum penalty for image restoration

In the field of image restoration, non-convex penalties and non-local self-similarity (NSS) prior have been found to enhance image edges and textures. However, NSS-based methods often overlook the inherent variations within patch groups by treating them as a single entity for processing. Despite the existence of numerous convex or non-convex regularizers, few of them have been able to adaptively adjust penalty strength based on NSS information in order to preserve fine details in an image. To address this issue, we propose a novel group sparsity residual constraint model with weighted log-sum penalty (GSRC-Log) for image restoration in this paper. The proposed regularization term is parameterized by an adaptive scalar parameter that relates to NSS, allowing the model to prioritize high NSS group sparse coefficients while penalizing low NSS coefficients. For image denoising, we provide detailed analysis on the optimal condition of our proposed model and prove that it has a simple closed-form global solution. For image restoration tasks, we utilize the ADMM algorithm to solve the GSRC-Log problem and empirically verify its convergence. Extensive experimental results on both image denoising and compressive sensing (CS) recovery demonstrate that our proposed GSRC-Log outperforms many popular or state-of-the-art methods.

A sampling greedy average regularized Kaczmarz method for tensor recovery

AbstractRecently, a regularized Kaczmarz method has been proposed to solve tensor recovery problems. In this article, we propose a sampling greedy average regularized Kaczmarz method. This method can be viewed as a block or mini‐batch version of the regularized Kaczmarz method, which is based on averaging several regularized Kaczmarz steps with a constant or adaptive extrapolated step size. Also, it is equipped with a sampling greedy strategy to select the working tensor slices from the sensing tensor. We prove that our new method converges linearly in expectation and show that the sampling greedy strategy can exhibit an accelerated convergence rate compared to the random sampling strategy. Numerical experiments are carried out to show the feasibility and efficiency of our new method on various signal/image recovery problems, including sparse signal recovery, image inpainting, and image deconvolution.

Cipher-image compression by using compressive sensing and interweaving permutation

Recently, compressing cipher images by using compressive sensing (CS) has attracted a lot of attention. However, the previous CS-based works cannot provide satisfactory compression performance. In this article, a cipher-image compression scheme based on CS and interweaving permutation is proposed to address this concern. Before image compression, the nature image is down-sampled to generate a lot of patches by using interweaving permutation firstly and then each patch is encrypted by a scrambling matrix, where each patch is a down-sampled image. In this way, the encrypted patches are highly correlated from one to each other since they preserve the correlation of the original patches. Therefore, we can encode the cipher image by employing CS and differential pulse-code modulation (DPCM) in an efficient way. To reconstruct the image effectively, an iterative shrinkage-thresholding (IST) algorithm is developed. Compared with the previous CS-based works, our scheme achieves better ratio-distortion (R-D) performance.

The Impact of Dissolved Salts on the Erosion of Physically Purified Compacted Bentonite

Compressed bentonite is an appropriate cushion material for getting rid of spent nuclear waste below the surface storage. The contact of compressed bentonite with water, its immersion in water and subsequently its swelling into the neighboring gaps are the principal processes for the development of colloid fines. In this study, to examine the impact of ionic strength on the erosion of compacted bentonite, only the ionic power values of the water contacting the bentonite were changed by keeping the flow rates constant. Sodium chloride was used to change the ionic power of the water contacting the bentonite throughout the experiment. Turbidity meter (TM) was used to determine the amount of eroded particles. The dissolution of bentonite fragments is critical not only due to their physical stability but also due to the radioactive isotopes they contain. An experimentation methodology is introduced. The implemented flow rates were 0.06 ml/min and 0.22 ml/min, and the selected waters were distilled water and 0.05 M NaCl ionic strength water. The dry densities of the compressed bentonite samples used were 1.67 g/cm3, 1.72 g/cm3, 1.72 g/cm3 and 1.72 g/cm3. With distilled water, the total erosion value measured at the end of the 24th day using a flow rate of 0.06 ml/min was 1002.7 mg, whereas the final erosion value measured at the end of the 24th day using water containing 0.05 M NaCl salt was 31.13 mg. In the case of distilled water, the total erosion value measured at the end of the 24th day using a flow rate of 0.22 ml/min was 1774.85 mg, while the total erosion value measured at the end of the 24th day using water containing 0.05 M NaCl salt was 73.6 mg. This demonstrates that the influence of the ionic strongness of the water on erosion is too important to be neglected.

Multiple Choice Hard Thresholding Pursuit (MCHTP) for simultaneous sparse recovery and sparsity order estimation

In this work, we propose a new greedy algorithm, referred to as the Multiple Choice Hard Thresholding Pursuit (MCHTP) which recovers a sparse vector from compressed linear measurements without explicit knowledge of its sparsity. MCHTP achieves this by suitably combining the steps of hard thresholding pursuit (HTP) with a novel sparsity selection criterion to iteratively select one among two possible sparsity values and subsequently recovering the unknown sparse vector along with its unknown sparsity order. We provide provable theoretical guarantees which ensure that MCHTP can estimate the sparsity order as well as the unknown sparse vector exactly from linear measurements. We also propose an extension of MCHTP, referred to as MCHTP−d, which can provide finer control on the estimated sparsity by tuning the parameter d. The simulation results corroborate the theoretical findings demonstrating the superior performance of MCHTP and MCHTP−d compared to state-of-the-art techniques in terms of sparse recovery and sparsity order estimation.

A single-pixel imaging method via low-resolution illumination patterns

Focusing on the field of single-pixel imaging for reconstructing high-resolution images, most existing methods end-to-end employ illumination patterns and reconstructed images of the same resolution, resulting in a singular imaging resolution. Crucially, in actual test environments, enhancing the resolution of illuminating patterns and increasing sampling times tends to introduce more disturbance information, consequently affecting the clarity of the reconstructed images. Therefore, this study proposes a single-pixel imaging method via low-resolution illuminating patterns. The method employs a small number of low-resolution illuminating patterns for compressed sampling of the targe, acquiring rough light signals with less disturbance interference, and directly generating a high-resolution image, termed Coarse Sampling Single-Pixel Imaging (CSSPI). The results show that the CSSPI method proposed in this paper demonstrates a 40.00% reduction in the amount of sampling information when compared to OMP, TVAL3, DLBOGI, and DSPINet. In simulation experiments with a salt-and-pepper noise ratio of 0.00–15.00%, or actual tests with smoke concentration ranging from 0 to 32 g/cm3, the CSSPI employing the low-resolution illumination pattern scheme for 4-times resolution reconstruction, consistently demonstrates relatively better imaging stability and clarity. The introduction of this method could potentially provide a modest contribution to the study of stable imaging for single-pixel technology in practical applications.

Noise reduction of axial piston motors using multi-objective optimization of reinforcing ribs based on identification of acoustic sources

The optimization of the housing for reducing vibration and noise in axial piston motors is facing challenges related to inaccurate locations of acoustic sources and inappropriate optimization parameters. In this study, a multi-objective optimization of the thicknesses of the reinforcing ribs for reducing the noise of axial piston motors is investigated by using the compression sensing (CS) method and response surface methodology (RSM). Combined with the CS method, the high-resolution reconstruction of sound-intensity images is used to guide the structural optimization areas through locations of acoustic sources. To reduce vibration and noise, the variable rib structure model (VRSM) is established in structural optimization areas. The thicknesses of reinforcing ribs in different areas are considered optimization variables, while the motor housing's peak vibration acceleration obtained by coupling the motor's dynamic model with the hydraulic model is utilized as the objective function. The mathematical relationship between these variables and the objective function is established through the RSM. Utilizing these functions, a multi-objective optimization model is formulated for discretizing the thicknesses of reinforcing ribs to reduce noise, employing a multi-objective genetic algorithm (MOGA) for optimization calculations. Finally, comparing the sound pressure levels of the axial piston motor with and without the optimized reinforcing ribs, the experimental results demonstrate a notable reduction in noise with the optimized reinforcing ribs. Specifically, there's a reduction of 2.7 dB at the peak frequency of 610 Hz.

Deep-learning-based reconstruction of T2-weighted magnetic resonance imaging of the prostate accelerated by compressed sensing provides improved image quality at half the acquisition time.

Deep-learning-based reconstruction (DLR) improves the quality of magnetic resonance (MR) images which allows faster acquisitions. The aim of this study was to compare the image quality of standard and accelerated T2 weighted turbo-spin-echo (TSE) images of the prostate reconstructed with and without DLR and to find associations between perceived image quality and calculated image characteristics. In a cohort of 47 prospectively enrolled consecutive patients referred for bi-parametric prostate magnetic resonance imaging (MRI), two T2-TSE acquisitions in the transverse plane were acquired on a 3T scanner-a standard T2-TSE sequence and a short sequence accelerated by a factor of two using compressed sensing (CS). The images were reconstructed with and without DLR in super-resolution mode. The image quality was rated in six domains. Signal-to-noise ratio (SNR), and image sharpness were measured. The mean acquisition time was 281±23 s for the standard and 140±12 s for the short acquisition (P<0.0001). DLR images had higher sharpness compared to non-DLR (P<0.001). Short and short-DLR had lower SNR than the standard and standard-DLR (P<0.001). The perceived image quality of short-DLR was rated better in all categories compared to the standard sequence (P<0.001 to P=0.004). All domains of subjective evaluation were correlated with measured image sharpness (P<0.001). T2-TSE acquisition of the prostate accelerated using CS combined with DLR reconstruction provides images with increased sharpness that have a superior quality as perceived by human readers compared to standard T2-TSE. The perceived image quality is correlated with measured image contrast.

Multi-Frequency Spherical Near-Field Antenna Measurements Using Compressive Sensing

Multi-Frequency Spherical Near-Field Antenna Measurements Using Compressive Sensing

Multiple Complementary Priors for Multispectral Image Compressive Sensing Reconstruction.

Compressive sensing (CS) techniques using a few compressed measurements have drawn considerable interest in reconstructing multispectral imagery (MSI). Nonlocal-based tensor methods have been widely used for MSI-CS reconstruction, which employ the nonlocal self-similarity (NSS) property of MSI to obtain satisfactory results. However, such methods only consider the internal priors of MSI while ignoring important external image information, for example deep-driven priors learned from a corpus of natural image datasets. Meanwhile, they usually suffer from annoying ringing artifacts due to the aggregation of overlapping patches. In this article, we propose a novel approach for highly effective MSI-CS reconstruction using multiple complementary priors (MCPs). The proposed MCP jointly exploits nonlocal low-rank and deep image priors under a hybrid plug-and-play framework, which contains multiple pairs of complementary priors, namely, internal and external, shallow and deep, and NSS and local spatial priors. To make the optimization tractable, a well-known alternating direction method of multiplier (ADMM) algorithm based on the alternating minimization framework is developed to solve the proposed MCP-based MSI-CS reconstruction problem. Extensive experimental results demonstrate that the proposed MCP algorithm outperforms many state-of-the-art CS techniques in MSI reconstruction. The source code of the proposed MCP-based MSI-CS reconstruction algorithm is available at: https://github.com/zhazhiyuan/MCP_MSI_CS_Demo.git.

Efficient gridless 2D DOA estimation based on generalized matrix‐form atomic norm minimization

AbstractTwo‐dimensional (2D) direction‐of‐arrival (DOA) estimation is crucial in array signal processing. Compressed sensing (CS) provides a superior alternative to spatial spectrum estimation algorithms by enabling 2D DOA estimation of correlated sources from single snapshot data. However, the grid mismatch effect inherent in grid‐based CS algorithms impacts estimation accuracy. Despite recent advancements, the state‐of‐the‐art gridless CS algorithm, decoupled atomic norm minimization, is limited to specific 2D array geometries, such as uniform rectangular arrays. This letter presents an efficient gridless 2D DOA estimation algorithm for generalized rectangular arrays, including both uniform and sparse arrays. The proposed algorithm achieves high accuracy through a novel approach called generalized matrix‐form atomic norm minimization and provides a fast solution using the alternating direction method of multipliers. Validation through computer simulations and practical experiments underscores its efficacy.

A novel thermal turbulence reconstruction method using proper orthogonal decomposition and compressed sensing coupled based on improved particle swarm optimization for sensor arrangement

With the development of offshore wind turbine single power toward levels beyond 10 MW, the increase in heat loss of components in the nacelle leads to a high local temperature in the nacelle, which seriously affects the performance of the components. Accurate reconstruction and control of thermal turbulence in the nacelle can alleviate this problem. However, the physical environment of thermal turbulence in the nacelle is very complex. Due to the intermittent and fluctuating nature of turbulence, the turbulent thermal environment is highly nonlinear when coupled with the temperature field. This leads to large reconstruction errors in existing reconstruction methods. Therefore, we improve the sparse reconstruction method for compressed sensing (CS) based on the concept of virtual time using proper orthogonal decomposition (POD). The POD-CS method links the turbulent thermal environment reconstruction with matrix decomposition to ensure computational accuracy and computational efficiency. The improved particle swarm optimization (PSO) is used to optimize the sensor arrangement to ensure stability of the reconstruction and to save sensor resources. We apply this novel and improved PSO-POD-CS coupled reconstruction method to the thermal turbulence reconstruction in the nacelle. The effects of different basis vector dimensions and different sensor location arrangements (boundary and interior) on the reconstruction errors are also evaluated separately, and finally, the desired reconstruction accuracy is obtained. The method is of research value for the reconstruction of conjugate heat transfer problems with high turbulence intensity.

Cipher-image coding via 2D compressive sensing and cipher-domain mapping

Recently, cipher-image coding via compressive sensing (CS) has received extensive attention. However, the previous schemes cannot provide satisfactory compression performance. In this article, a cipher-image coding scheme based on 2D compressive sensing (2DCS) and cipher-domain mapping (CDM) is proposed to address this concern. Before image compression, the 2D image is encrypted by the scrambling operation to protect privacy. Then, with the aid of auxiliary information (AI), the ciphertext image is mapped by CDM to facilitate cipher-image compression. Thirdly, the mapped ciphertext image is compressed by using 2DCS. Finally, the mapped CS measurements are encoded into bits. Since CDM operation can make the amplitude scale of CS measurements smaller, the mapped CS measurements can be encoded with fewer bits than the raw CS measurements. Simulation results show that this work achieves better compression performance than the previous CS-based works.

Learned Two-Step Iterative Shrinkage Thresholding Algorithm for Deep Compressive Sensing

Learned Two-Step Iterative Shrinkage Thresholding Algorithm for Deep Compressive Sensing

Channel Estimation and Pilot Overhead Reduction in OFDM Systems Using Compressed Sensing Dynamic Mode Decomposition

Channel Estimation and Pilot Overhead Reduction in OFDM Systems Using Compressed Sensing Dynamic Mode Decomposition

Image Compression Based on Near Lossless Predictive Measurement Coding for Block-Based Compressive Sensing

Image Compression Based on Near Lossless Predictive Measurement Coding for Block-Based Compressive Sensing

Improved Magnetic Resonance Image Reconstruction using Compressed Sensing and Adaptive Multi Extreme Particle Swarm Optimization Algorithm

One powerful technique that can offer a thorough examination of the body's internal structure is magnetic resonance imaging (MRI). MRI's lengthy acquisition times, however, may restrict its clinical usefulness, particularly in situations where time is of the essence. Compressed sensing (CS) has emerged as a potentially useful method for cutting down on MRI acquisition times; nevertheless, the effectiveness of CS-MRI is dependent on the selection of the sparsity-promoting algorithm and sampling scheme. This research paper presents a novel method based on adaptive multi-extreme particle swarm optimization (AMEPSO) and dual tree complex wavelet transform (DTCWT) for fast image acquisition in magnetic resonance. The method uses AMEPSO in order to maximize the sampling pattern and minimize reconstruction error, while also exploiting the sparsity of MR images in the DTCWT domain to improve directional selectivity and shift invariance. MATLAB software was used for simulation of the proposed method. In comparison with the particle swarm optimized-DTCWT (PSODTCWT) and DTCWT algorithms, respectively, the results demonstrated an improvement in the peak signal-to-noise ratio of 8.92% and 15.92% and a higher structural similarity index measure of 3.69% and 7.5%. Based on these improvements, the proposed method could potentially make high-quality, real-time MRI imaging possible, which might improve detection and treatment of medical conditions and increase the throughput of MRI machines.

Iterative Adaptive Based Multi-Polarimetric SAR Tomography of the Forested Areas

Synthetic aperture radar tomography (TomoSAR) is an extension of synthetic aperture radar (SAR) imaging. It introduces the synthetic aperture principle into the elevation direction to achieve three-dimensional (3-D) reconstruction of the observed target. Compressive sensing (CS) is a favorable technology for sparse elevation recovery. However, for the non-sparse elevation distribution of the forested areas, if CS is selected to reconstruct it, it is necessary to utilize some orthogonal bases to first represent the elevation reflectivity sparsely. The iterative adaptive approach (IAA) is a non-parametric algorithm that enables super-resolution reconstruction with minimal snapshots, eliminates the need for hyperparameter optimization, and requires fewer iterations. This paper introduces IAA to tomographicinversion of the forested areas and proposes a novel multi-polarimetric-channel joint 3-D imaging method. The proposed method relies on the characteristics of the consistent support of the elevation distribution of different polarimetric channels and uses the L2-norm to constrain the IAA-based 3-D reconstruction of each polarimetric channel. Compared with typical spectral estimation (SE)-based algorithms, the proposed method suppresses the elevation sidelobes and ambiguity and, hence, improves the quality of the recovered 3-D image. Compared with the wavelet-based CS algorithm, it reduces computational cost and avoids the influence of orthogonal basis selection. In addition, in comparison to the IAA, it demonstrates greater accuracy in identifying the support of the elevation distribution in forested areas. Experimental results based on BioSAR 2008 data are used to validate the proposed method.