Compressed Sensing Reconstruction Research Articles

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.

Structured residual sparsity for video compressive sensing reconstruction

Recent advancements in the residual sparsity strategy have garnered widespread attention in video compressive sensing (CS) reconstruction. However, most of the existing residual sparsity-based video CS reconstruction methods usually suffer from some limitations that lead to undesired visual artifacts. Firstly, these methods only rely on a patch sparsity scheme that is limited by their focus on the local structures of each video frame, neglecting the nonlocal self-similarity (NSS) property inherent to each video frame. Secondly, these methods concentrate on utilizing the NSS property of external reference frames for multi-hypothesis (MH) prediction while disregarding the internal NSS property of the current frame. In this paper, we propose a new structured residual sparsity (SRS) approach for video CS reconstruction, which jointly exploits the NSS properties of the current frame and its reference frames. Specifically, due to the unavailability of the original video frames, we first devise an effective intraframe CS (EICS) reconstruction method that leverages the internal NSS property of each frame. This approach enables us to obtain initial recovery frames, which then facilitate the execution of MH prediction. Following this, we generate a residual frame for the current frame by employing the MH prediction. Then, we propose a novel SRS model jointly using the NSS properties of the current frame and its reference frames to explore both the correlations of intraframe and interframe for reconstructing the current frame. Furthermore, for the sake of optimization feasibility, we develop an effective alternating direction method of multipliers (ADMM) algorithm to address the objective. Our experimental findings reveal that the proposed SRS not only yields superior quantitative results, but also uncovers finer details and causes fewer visual artifacts compared to many popular or state-of-the-art video CS reconstruction approaches.

Compressed Sensing Image Reconstruction with Fast Convolution Filtering

Image reconstruction is a crucial aspect of computational imaging. The compressed sensing reconstruction (CS) method has been developed to obtain high-quality images. However, the CS method is commonly time-consuming in image reconstruction. To overcome this drawback, we propose a compressed sensing reconstruction method with fast convolution filtering (F-CS method), which significantly increases reconstruction speed by reducing the number of convolution operations without image fill. The experimental results show that by using the F-CS method, the reconstruction speed can be increased by a factor of 7 compared to the conventional CS method. Moreover, the F-CS method proposed in this paper is compared with the back-propagation reconstruction (BP) method and super-resolution reconstruction (SR) method, and it is validated that the proposed method has a lower computational resource cost for high-quality image reconstruction and exhibits a much more balanced capability.

Digital Pathology Image Reconstruction with Alternating Direction Method of Multipliers using Wavelet, Contourlet and Shearlet Transforms

Digital pathology refers to image-based environment in which acquisition, extraction and interpretation of pathology information is supported by computational techniques. It has a huge potential to facilitate the diagnostic process, however, big data size and necessity of large storage areas are challenging. Therefore, in this research, Compressed Sensing (CS) scheme is studied with digital pathology images in order to reduce the amount of data for reconstruction. CS requires the sparsity of signals for a successful recovery which means that different sparsifying bases can alter the final performance. Wavelet, Contourlet and Shearlet Transforms are investigated to sparsify the digital pathology images, it is seen that Contourlet Transform is superior. Alternating Direction Method of Multipliers (ADMM) is chosen for reconstruction since it is a robust and fast convex optimization method. Despite the fact that digital pathology images are less sparse than classical images, CS reconstruction is satisfactory, which emphasizes the potential of CS for digital pathology. This study can be pioneering in the field of CS with digital pathology so it can encourage further studies of CS based imaging with different type of microscopes or at different wavelengths.

EIDNet: Extragradient-based iterative denoising network for image compressive sensing reconstruction

Compressive sensing (CS) is a kind of hardware-friendly technology in effective image reconstruction. Most of the existing CS reconstruction methods can be classified into model-driven iterative optimization methods and data-driven neural network methods. These two types of methods have their own problems with computational complexity and theoretical interpretability. Motivated by the deep unfolding theory, we develop the model-driven Extragradient-based Iterative Denoising Network, dubbed EIDNet, which is based on the denoising model of the iterative shrinkage threshold algorithm (ISTA). By unfolding the iterative denoising model into the deep learning network, EIDNet addresses the interpretability problem of neural network methods in CS reconstruction. Each denoising iteration of the optimization algorithm is mapped into one layer of the reconstruction network in EIDNet. The extragradient method is adopted to accelerate network convergence. In addition, we introduce a learning-based sampling and initialization network for adaptive sampling and initialization. Extensive experiments show that the proposed EIDNet can obtain better image CS reconstruction performance than other state-of-the-art CS methods while maintaining satisfactory reconstruction efficiency.

Multiply Complementary Priors for Image Compressive Sensing Reconstruction in Impulsive Noise

Impulsive noise is always present in real-world image Compressive Sensing (CS) acquisition systems, where existing CS reconstruction performance may seriously deteriorate. In this article, we propose a robust CS formulation for image reconstruction to suppress outliers in the presence of impulsive noise. To address this issue, we consider a novel truncated-Cauchy loss function as the metric of residual error to elevate the reconstruction robustness. Specifically, we design a complementary priors model to incorporate nonconvex nonlocal low-rank prior and deep denoiser prior for high-accuracy image reconstruction. By means of the half-quadratic optimization theory and generalized soft-thresholding technique, we also develop an alternative optimization algorithm for solving the induced nonconvex optimization problem. Numerical simulations demonstrate the robustness and accuracy of the proposed robust CS method compared to some recent CS methods for image reconstruction in impulsive noise.

FPGA Implementation of Threshold Projection Orthogonal Matching Pursuit Algorithm for Compressed Sensing Reconstruction

FPGA Implementation of Threshold Projection Orthogonal Matching Pursuit Algorithm for Compressed Sensing Reconstruction

Multi-image super-resolution based low complexity deep network for image compressive sensing reconstruction

Deep learning (DL) has been widely utilized in image compressive sensing (CS) to enhance the quality and speed of reconstruction. The typical deep network for CS reconstruction comprises an initial reconstruction subnetwork, followed by a cascaded deep refinement reconstruction subnetworks. This paper introduces a new low-complexity image CS deep reconstruction framework, GSRCS, which leverages multi-image based deep super-resolution technology to better address the cost constraints of practical applications. The proposed initial reconstruction module generates multiple low-resolution images in parallel by grouping the input measurements, while a high-quality, high-resolution reconstructed image is produced through a multi-image deep super-resolution network. The theoretical derivation and experimental results demonstrate that this method significantly reduces system complexity in terms of parameters and floating-point arithmetic operations, while achieving competitive reconstruction performance compared to the state-of-the-arts. Specifically, the average number of parameters is reduced by over 63%, and the computational complexity is decreased by more than 88%.

MsDC-DEQ-Net: Deep Equilibrium Model (DEQ) with Multiscale Dilated Convolution for Image Compressive Sensing (CS)

Compressive sensing (CS) is a technique that enables the recovery of sparse signals using fewer measurements than traditional sampling methods. To address the computational challenges of CS reconstruction, our objective is to develop an interpretable and concise neural network model for reconstructing natural images using CS. We achieve this by mapping one step of the iterative shrinkage thresholding algorithm (ISTA) to a deep network block, representing one iteration of ISTA. To enhance learning ability and incorporate structural diversity, we integrate aggregated residual transformations (ResNeXt) and squeeze-and-excitation mechanisms into the ISTA block. This block serves as a deep equilibrium layer connected to a semi-tensor product network for convenient sampling and providing an initial reconstruction. The resulting model, called MsDC-DEQ-Net, exhibits competitive performance compared to state-of-the-art network-based methods. It significantly reduces storage requirements compared to deep unrolling methods, using only one iteration block instead of multiple iterations. Unlike deep unrolling models, MsDC-DEQ-Net can be iteratively used, gradually improving reconstruction accuracy while considering computation tradeoffs. Additionally, the model benefits from multiscale dilated convolutions, further enhancing performance.

Secure Low-complexity Compressive Sensing with Preconditioning Prior Regularization Reconstruction

Compressive sensing (CS), a breakthrough technology in image processing, provides a privacy-preserving layer and image reconstruction while performing sensing and recovery processes, respectively. Unfortunately, it still faces high-complexity, low-security, and low-quality reconstruction challenges during image processing. Therefore, this article presents a secure low-complexity CS scheme with preconditioning prior regularization reconstruction. More specifically, the original image is compressed by a low-complexity LFSR-based sparse circulant matrix to obtain measurements. It is worth noting that measurements achieve preliminary distribution equalization through the Tanh sequence to acquire processed measurements. Furthermore, the privacy-preserving edge processing for processed measurements can achieve high security. Finally, preconditioning prior regularization CS reconstruction is designed to improve reconstruction performance. Simulation results and analyses demonstrate that the proposed scheme can achieve low-complexity sampling, high security, and superior reconstruction performance.

Accelerated multiple-quantum-filtered sodium magnetic resonance imaging using compressed sensing at 7 T

PurposeMultiple-quantum-filtered (MQF) sodium magnetic resonance imaging (MRI), such as enhanced single-quantum and triple-quantum-filtered imaging of 23Na (eSISTINA), enables images to be weighted towards restricted sodium, a promising biomarker in clinical practice, but often suffers from clinically infeasible acquisition times and low image quality. This study aims to mitigate the above limitation by implementing a novel eSISTINA sequence at 7 T with the application of compressed sensing (CS) to accelerate eSISTINA acquisitions without a noticeable loss of information. MethodsA novel eSISTINA sequence with a 3D spiral-based sampling scheme was implemented at 7 T for the application of CS. Fully sampled datasets were obtained from one phantom and ten healthy subjects, and were then retrospectively undersampled by various undersampling factors. CS undersampled reconstructions were compared to fully sampled and undersampled nonuniform fast Fourier transform (NUFFT) reconstructions. Reconstruction performance was evaluated based on structural similarity (SSIM), signal-to-noise ratio (SNR), weightings towards total and compartmental sodium, and in vivo quantitative estimates. ResultsCS-based phantom and in vivo images have less noise and better structural delineation while maintaining the weightings towards total, non-restricted (predominantly extracellular), and restricted (primarily intracellular) sodium. CS generally outperforms NUFFT with a higher SNR and a better SSIM, except for the SSIM in TQ brain images, which is likely due to substantial noise contamination. CS enables in vivo quantitative estimates with <15% errors at an undersampling factor of up to two. ConclusionsSuccessful implementation of an eSISTINA sequence with an incoherent sampling scheme at 7 T was demonstrated. CS can accelerate eSISTINA by up to twofold at 7 T with reduced noise levels compared to NUFFT, while maintaining major structural information, reasonable weightings towards total and compartmental sodium, and relatively reliable in vivo quantification. The associated reduction in acquisition time has the potential to facilitate the clinical applicability of MQF sodium MRI.

AdaCS: Adaptive Compressive Sensing with Restricted Isometry Property-Based Error-clamping.

Scene-dependent adaptive compressive sensing (CS) has been a long pursuing goal that has huge potential to significantly improve the performance of CS. However, with no access to the ground truth, how to design the scene-dependent adaptive strategy is still an open problem. In this paper, a restricted isometry property (RIP) condition-based error-clamping is proposed, which could directly predict the reconstruction error, i.e., the difference between the current-stage reconstructed image and the ground truth image, and adaptively allocate more samples to regions with larger reconstruction error at the next sampling stage. Furthermore, we propose a CS reconstruction network composed of Progressively inverse transform and Alternating Bi-directional Multi-grid Network, named PiABM-Net, that could efficiently utilize the multi-scale information for reconstructing the target image. The effectiveness of the proposed adaptive and cascaded CS method is demonstrated with extensive quantitative and qualitative experiments, compared with the state-of-the-art CS algorithms.

NesTD-Net: Deep NESTA-Inspired Unfolding Network With Dual-Path Deblocking Structure for Image Compressive Sensing.

Deep compressive sensing (CS) has become a prevalent technique for image acquisition and reconstruction. However, existing deep learning (DL)-based CS methods often encounter challenges such as block artifacts and information loss during iterative reconstruction, particularly at low sampling rates, resulting in a reduction of reconstructed details. To address these issues, we propose NesTD-Net, an unfolding-based architecture inspired by the NESTA algorithm, designed for image CS. NesTD-Net integrates DL modules into NESTA iterations, forming a deep network that continuously iterates to minimize the l1 -norm CS problem, ensuring high-quality image CS. Utilizing a learned sampling matrix for measurements and an initialization module for initial estimate, NesTD-Net then introduces Iteration Sub-Modules derived from the NESTA algorithm (i.e., Yk , Zk , and Xk ) during reconstruction stages to iteratively solve the l1 -norm CS reconstruction. Additionally, NesTD-Net incorporates a Dual-Path Deblocking Structure (DPDS) to facilitate feature information flow and mitigate block artifacts, enhancing image detail reconstruction. Furthermore, DPDS exhibits remarkable versatility and demonstrates seamless integration with other unfolding-based methods, offering the potential to enhance their performance in image reconstruction. Experimental results demonstrate that our proposed NesTD-Net achieves better performance compared to other state-of-the-art methods in terms of image quality metrics such as SSIM and PSNR, as well as visual perception on several public benchmark datasets.

Optimal Protocol for Contrast-enhanced Free-running 5D Whole-heart Coronary MR Angiography at 3T.

Free-running 5D whole-heart coronary MR angiography (MRA) is gaining in popularity because it reduces scanning complexity by removing the need for specific slice orientations, respiratory gating, or cardiac triggering. At 3T, a gradient echo (GRE) sequence is preferred in combination with contrast injection. However, neither the injection scheme of the gadolinium (Gd) contrast medium, the choice of the RF excitation angle, nor the dedicated image reconstruction parameters have been established for 3T GRE free-running 5D whole-heart coronary MRA. In this study, a Gd injection scheme, RF excitation angles of lipid-insensitive binominal off-resonance RF excitation (LIBRE) pulse for valid fat suppression and continuous data acquisition, and compressed-sensing reconstruction regularization parameters were optimized for contrast-enhanced free-running 5D whole-heart coronary MRA using a GRE sequence at 3T. Using this optimized protocol, contrast-enhanced free-running 5D whole-heart coronary MRA using a GRE sequence is feasible with good image quality at 3T.

Achieving Robust Compressive Sensing Seismic Acquisition with a Two-Step Sampling Approach

The compressive sensing (CS) framework offers a cost-effective alternative to dense alias-free sampling. Designing seismic layouts based on the CS technique imposes the use of specific sampling patterns in addition to the logistical and geophysical requirements. We propose a two-step design process for generating CS-based schemes suitable for seismic applications. During the first step, uniform random sampling is used to generate a random scheme, which is supported theoretically by the restricted isometry property. Following that, designated samples are added to the random scheme to control the maximum distance between adjacent sources (or receivers). The null space property theoretically justifies the additional samples of the second step. Our sampling method generates sampling patterns with a CS theoretical background, controlled distance between adjacent samples, and a flexible number of active and omitted samples. The robustness of two-step sampling schemes for reallocated samples is investigated and CS reconstruction tests are performed. In addition, using this approach, a CS-based 3D seismic survey is designed, and the distributions of traces in fold maps and rose diagrams are analyzed. It is shown that the two-step scheme is suitable for CS-based seismic surveys and field applications.

A temporal Convolutional Network for EMG compressed sensing reconstruction

Electromyography (EMG) plays a vital role in detecting medical abnormalities and analyzing the biomechanics of human or animal movements. However, long-term EMG signal monitoring will increase the bandwidth requirements and transmission system burden. Compressed sensing (CS) is attractive for resource-limited EMG signal monitoring. However, traditional CS reconstruction algorithms require prior knowledge of the signal, and the reconstruction process is inefficient. To solve this problem, this paper proposed a reconstruction algorithm based on deep learning, which combines the Temporal Convolutional Network (TCN) and the fully connected layer to learn the mapping relationship between the compressed measurement value and the original signal, and it has been verified in the Ninapro database. The results show that, for the same subject, compared with the traditional reconstruction algorithms orthogonal matching pursuit (OMP), basis pursuit (BP), and Modified Compressive Sampling Matching Pursuit (MCo), the reconstruction quality and efficiency of the proposed method is significantly improved under various compression ratios (CR).

Multi-Channel Representation Learning Enhanced Unfolding Multi-Scale Compressed Sensing Network for High Quality Image Reconstruction.

Deep Unfolding Networks (DUNs) serve as a predominant approach for Compressed Sensing (CS) reconstruction algorithms by harnessing optimization. However, a notable constraint within the DUN framework is the restriction to single-channel inputs and outputs at each stage during gradient descent computations. This constraint compels the feature maps of the proximal mapping module to undergo multi-channel to single-channel dimensionality reduction, resulting in limited feature characterization capabilities. Furthermore, most prevalent reconstruction networks rely on single-scale structures, neglecting the extraction of features from different scales, thereby impeding the overall reconstruction network's performance. To address these limitations, this paper introduces a novel CS reconstruction network termed the Multi-channel and Multi-scale Unfolding Network (MMU-Net). MMU-Net embraces a multi-channel approach, featuring the incorporation of Adap-SKConv with an attention mechanism to facilitate the exchange of information between gradient terms and enhance the feature map's characterization capacity. Moreover, a Multi-scale Block is introduced to extract multi-scale features, bolstering the network's ability to characterize and reconstruct the images. Our study extensively evaluates MMU-Net's performance across multiple benchmark datasets, including Urban100, Set11, BSD68, and the UC Merced Land Use Dataset, encompassing both natural and remote sensing images. The results of our study underscore the superior performance of MMU-Net in comparison to existing state-of-the-art CS methods.

The A*orthogonal least square algorithm with the self-training dictionary for propeller signals reconstruction

The transmission of huge propeller signals via underwater wireless networks has high energy consumption, and conventional compression methods based on Nyquist sampling theorem cannot achieve efficient compression. Different from conventional compression methods, compressed sensing (CS) realizes the sub-Nyquist sampling rate, but the sparse signal is one of the preconditions of CS. Unfortunately, propeller signals are always non-sparse in both time and frequency domains. Therefore, the commonly used fixed dictionary is not suitable for sparse representation of propeller signals. To improve sparse representation, this paper proposes a self-training dictionary (STD) scheme, which updates the dictionary and sparse encoding simultaneously in iterations. Combining with the STD scheme, a CS reconstruction based on A*orthogonal least square (A*OLS) is proposed. In detail, a candidate subset selected by the orthogonal least square (OLS) algorithm is used as the node of the tree, and the search tree is established by A*search to find the optimal sparse solution. The experimental results confirm that the STD-A*OLS framework has significant advantages in performance including recovered signal-to-noise ratio (RSNR), percent norm difference (PND), and structure similarity index measure (SSIM).

A New ACD-OMP Accelerator With Clustered Computing Look-Ahead

The orthogonal matching pursuit (OMP) has been widely explored to realize real-time compressed sensing (CS) reconstruction. The matrix pseudo-inverse of the least squares (LSs) is the most computationally complex operation in the OMP. Among various algorithms to realize this complex operation, the alternative Cholesky decomposition (ACD) algorithm performs the best. However, it typically involves a very long computation time due to its iterative procedure. To accelerate the ACD-OMP algorithm, a novel method called clustered computing look-ahead (CCL) is proposed. Inspired by the famous parallel carry look-ahead adder (CLA), CCL adds a propagation matrix to decouple the data dependency in ACD and then uses a clustering operator to transform the iterative computation of ACD into a pipelined and parallelized computation. This brief also proposes an efficient hardware architecture of the CCL-based ACD-OMP algorithm for CS reconstruction. The proposed algorithm is implemented on field programmable gate array (FPGA). For sparse signals with the same sparsity and length, the proposed implementation is 1.96 times faster than state-of-the-art work.

Compressed sensing framework for BCG signals based on the optical fiber sensor.

A compressed sensing (CS) framework is built for ballistocardiography (BCG) signals, which contains two parts of an optical fiber sensor-based heart monitoring system with a CS module and an end-to-end deep learning-based reconstruction algorithm. The heart monitoring system collects BCG data, and then compresses and transmits the data through the CS module at the sensing end. The deep learning-based algorithm reconstructs compressed data at the received end. To evaluate results, three traditional CS reconstruction algorithms and a deep learning method are adopted as references to reconstruct the compressed BCG data with different compression ratios (CRs). Results show that our framework can reconstruct signals successfully when the CR grows from 50% to 95% and outperforms other methods at high CRs. The mean absolute error (MAE) of the estimated heartbeat rate (HR) is lower than 1 bpm when the CR is below 95%. The proposed CS framework for BCG signals can be integrated into the IoMT system, which has great potential in health care for both medical and home use.