Compressed Sensing Method Research Articles

A 3D fast MR elastography sequence with interleaved multislab acquisition and Hadamard encoding.

To enhance the functional capability of MRI, this study aims to develop a novel MR elastography (MRE) sequence that achieves rapid acquisition without distortion artifacts. A displacement-encoded stimulated echo (DENSE) with multiphase acquisition scheme was used to capture wave images. A center-out golden-angle stack-of-stars sampling pattern was introduced for improved SNR and data incoherence. A combination of Hadamard encoding and interleaved multislab acquisition schemes was used to increase the acquisition efficiency of MRE data with multiple directions and phase offsets. A generalized parallel-imaging and compressed-sensing method was further applied to accelerate the acquisition process. The imaging results of the proposed sequence were compared with those from six gradient echo (GRE)/EPI/DENSE-based MRE sequences via phantom and brain acquisitions. The proposed sequence achieved a 6-fold acceleration compared with GRE MRE. With the application of a conventional parallel-imaging and compressed-sensing algorithm, the scanning speed was further accelerated by 8-fold, matching the speed of EPI-based MRE. Phantom tests revealed small variances in stiffness measurements across the seven sequences (< 9.23%). The proposed sequence exhibited a higher contrast-to-noise ratio (1.38) than the two EPI-based sequences (0.61/0.76) and similar to GRE-based sequences (1.34/1.22/1.58). Brain imaging validated the effectiveness of the proposed sequence in accurate stiffness estimation and distortion artifact avoidance. A rapid DENSE-based MRE sequence with interleaved multislab acquisition and Hadamard encoding was developed at a speed matching EPI-based sequences, without compromising SNR or introducing distortion artifacts.

A dictionary learning based unsupervised neural network for single image compressed sensing

In the field of Compressed Sensing (CS), the sparse representation of signals and the advancement of reconstruction algorithms are two critical challenges. However, conventional CS algorithms often fail to sufficiently exploit the structured sparsity present in images and suffer from poor reconstruction quality. Most deep learning-based CS methods are typically trained on large-scale datasets. Obtaining a sufficient number of training sets is challenging in many practical applications and there may be no training sets available at all in some cases. In this paper, a novel deep Dictionary Learning (DL) based unsupervised neural network for single image CS (dubbed DL-CSNet) is proposed. It is an effective trainless neural network that consists of three components and their corresponding loss functions: 1) a DL layer that consists of multi-layer perceptron (MLP) and convolution neural networks (CNN) for latent sparse features extraction with the L1-norm sparsity loss function; 2) an image smoothing layer with the Total Variation (TV) like image smoothing loss function; and 3) a CS acquisition layer for image compression, with the Mean Square Error (MSE) loss function between the original image compression and the reconstructed image compression. In particular, the proposed DL-CSNet is a lightweight and fast model that does not require datasets for training and exhibits a fast convergence speed, making it suitable for deployment in resource-constrained environments. Experiments have demonstrated that the proposed DL-CSNet achieves superior performance compared to traditional CS methods and other unsupervised state-of-the-art deep learning-based CS methods.

Hybrid Transformer and Convolution for Image Compressed Sensing

In recent years, deep unfolding networks (DUNs) have received widespread attention in the field of compressed sensing (CS) reconstruction due to their good interpretability and strong mapping capabilities. However, existing DUNs often improve the reconstruction effect at the expense of a large number of parameters, and there is the problem of information loss in long-distance feature transmission. Based on the above problems, we propose an unfolded network architecture that mixes Transformer and large kernel convolution to achieve sparse sampling and reconstruction of natural images, namely, a reconstruction network based on Transformer and convolution (TCR-Net). The Transformer framework has the inherent ability to capture global context through a self-attention mechanism, which can effectively solve the challenge of long-range dependence on features. TCR-Net is an end-to-end two-stage architecture. First, a data-driven pre-trained encoder is used to complete the sparse representation and basic feature extraction of image information. Second, a new attention mechanism is introduced to replace the self-attention mechanism in Transformer, and a hybrid Transformer and convolution module based on optimization-inspired is designed. Its iterative process leads to the unfolding framework, which approximates the original image stage by stage. Experimental results show that TCR-Net outperforms existing state-of-the-art CS methods while maintaining fast computational speed. Specifically, when the CS ratio is 0.10, the average PSNR on the test set used in this paper is improved by at least 0.8%, the average SSIM is improved by at least 1.5%, and the processing speed is higher than 70FPS. These quantitative results show that our method has high computational efficiency while ensuring high-quality image restoration.

A signal-adaptive measurement matrix construction algorithm for compressed sensing of sEMG data

Abstract Surface electromyography (sEMG), serving as a pivotal wearable technology, is a promising tool to assess and monitor muscle function. Yet, the efficacy of a sEMG system faces inevitable constraints, primarily stemming from the challenges of transmission and energy consumption induced by big data. Compressed sensing (CS) is a promising data acquisition solution that takes advantage of the signal sparseness in a particular basis to significantly reduce the number of samples. Current CS methods usually employ random or deterministic measurement matrix to compress sEMG signal. However, these measurement matrices do not integrate the signal feature, which limits the performance of these CS methods. To address this problem, this paper proposes an improved CS method for sEMG data compression. This proposed method introduces a measurement matrix construction algorithm to produce a deterministic matrix tailored for processing sEMG signals. The deterministic measurement matrix integrates the characteristics of the magnitudes of sEMG signals. The sEMG signals acquired from the upper limb muscles of the stroke survivors were applied to evaluate the proposed CS method, with results showing that it achieves better reconstruction accuracy and robustness than the CS methods with other measurement matrices. The proposed method employing basis pursuit (BP) in the signal reconstruction presents better performance than that employing orthogonal matching pursuit (OMP). Hence, we can conclude that the proposed CS algorithm is of key importance for the popularization of sEMG in the wearable health monitoring devices.&amp;#xD;

LD-CSNet: A latent diffusion-based architecture for perceptual Compressed Sensing

Compressed Sensing (CS) is a groundbreaking paradigm in image acquisition, challenging the constraints of the Nyquist–Shannon sampling theorem. This enables high-quality image reconstruction using a minimal number of measurements. Neural Networks’ potent feature induction capabilities enable advanced data-driven CS methods to achieve high-fidelity image reconstruction. However, achieving satisfactory reconstruction performance, particularly in terms of perceptual quality, remains challenging at extremely low sampling rates. To tackle this challenge, we introduce a novel two-stage image CS framework based on latent diffusion, named LD-CSNet. In the first stage, we utilize an autoencoder pre-trained on a large dataset to represent natural images as low-dimensional latent vectors, establishing prior knowledge distinct from sparsity and effectively reducing the dimensionality of the solution space. In the second stage, we employ a conditional diffusion model for maximum likelihood estimates in the latent space. This is supported by a measurement embedding module designed to encode measurements, making them suitable for a denoising network. This guides the generation process in reconstructing low-dimensional latent vectors. Finally, the image is reconstructed using a pre-trained decoder. Experimental results across multiple public datasets demonstrate LD-CSNet’s superior perceptual quality and robustness to noise. It maintains fidelity and visual quality at lower sampling rates. Research findings suggest the promising application of diffusion models in image CS. Future research can focus on developing more appropriate models for the first stage.

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.

Enhanced Channel Estimation Performance-Based Intelligent Reflecting Surface Massive MIMO Systems

Intelligent reflecting surfaces (IRS) are an innovative technique that dramatically increases system efficiency. The integration of massive multiple-input multiple-output (massive MIMO) and IRS has been considered the most efficient route to 6G networks. An important challenge in IRS-aided massive MIMO wireless systems is channel estimation. With a rise in the number of IRS-reflecting elements and IRS-assisted users, channel training overhead becomes too large, resulting in large transmission delays and poor data transfer rates. To overcome this problem, an enhanced compressive sensing (CS) method to determine reliable channel state information (CSI) in IRS-aided massive MIMO systems is proposed, which combines enhanced compressive sensing with a deep denoising convolution neural network (CsiNet-DeCNN). By using deep learning methods to denoise channel data, our proposed model is validated numerically, indicating that it is accurate with low NMSE. Further, the results indicate that CsiNet-DeCNN performs better than traditional CS methods in estimating channel parameters.

Transformer based Douglas-Rachford unrolling network for compressed sensing

Compressed sensing (CS) with the binary sampling matrix is hardware-friendly and memory-saving in the signal processing field. Existing Convolutional Neural Network (CNN)-based CS methods show potential restrictions in exploiting non-local similarity and lack interpretability. In parallel, the emerging Transformer architecture performs well in modelling long-range correlations. To further improve the CS reconstruction quality from highly under-sampled CS measurements, a Transformer based deep unrolling reconstruction network abbreviated as DR-TransNet is proposed, whose design is inspired by the traditional iterative Douglas-Rachford algorithm. It combines the merits of structure insights of optimization-based methods and the speed of the network-based ones. Therein, a U-type Transformer based proximal sub-network is elaborated to reconstruct images in the wavelet domain and the spatial domain as an auxiliary mode, which aims to explore local informative details and global long-term interaction of the images. Specially, a flexible single model is trained to address the CS reconstruction with different binary CS sampling ratios. Compared with the state-of-the-art CS reconstruction methods with the binary sampling matrix, the proposed method can achieve appealing improvements in terms of Peak Signal to Noise Ratio (PSNR), Structural Similarity Index Measure (SSIM) and visual metrics. Codes are available at https://github.com/svyueming/DR-TransNet.

Enhancing quality and speed in database-free neural network reconstructions of undersampled MRI with SCAMPI.

We present SCAMPI (Sparsity Constrained Application of deep Magnetic resonance Priors for Image reconstruction), an untrained deep Neural Network for MRI reconstruction without previous training on datasets. It expands the Deep Image Prior approach with a multidomain, sparsity-enforcing loss function to achieve higher image quality at a faster convergence speed than previously reported methods. Two-dimensional MRI data from the FastMRI dataset with Cartesian undersampling in phase-encoding direction were reconstructed for different acceleration rates for single coil and multicoil data. The performance of our architecture was compared to state-of-the-art Compressed Sensing methods and ConvDecoder, another untrained Neural Network for two-dimensional MRI reconstruction. SCAMPI outperforms these by better reducing undersampling artifacts and yielding lower error metrics in multicoil imaging. In comparison to ConvDecoder, the U-Net architecture combined with an elaborated loss-function allows for much faster convergence at higher image quality. SCAMPI can reconstruct multicoil data without explicit knowledge of coil sensitivity profiles. Moreover, it is a novel tool for reconstructing undersampled single coil k-space data. Our approach avoids overfitting to dataset features, that can occur in Neural Networks trained on databases, because the network parameters are tuned only on the reconstruction data. It allows better results and faster reconstruction than the baseline untrained Neural Network approach.

A multi-channel ECG signal deep compressive sensing method using Treeshaped Autoecoder based on multiscale feature fusion

Conventionally, multi-lead Electrocardiogram (ECG) signals are recorded and stored using high sensing rates and high precision, resulting in huge data volumes and placing greater pressure on storage and transmission resources. Compressive sensing (CS) allows efficient encoding and decoding of signals through sparse representation, measurement and reconstruction for compressed storage and transmission of ECG signals. Traditional CS methods generally requires manually selecting the features or dictionaries used in sparse representations, which lacks adaptivity and flexibility, and the complexity of the reconstruction process limits the application of CS in some scenarios with high real-time requirements. In this paper, we propose a deep compressive sensing framework for processing multi-lead ECG signals by combining CS and deep learning, which is based on multi-scale feature fusion to construct a binary tree-shaped autoencoder architecture to achieve efficient compression and reconstruction of ECG signals. Experiments on the PTB diagnostic ECG database show that the proposed method achieves “very good” reconstruction quality at low sensing rates, with PRD and SNR of 1.77 % and 35.67 dB, respectively, when SR = 20 %. In addition, we investigate how the number of quantization bits affects the quality of reconstructed signals. After analysis, we found that 8-bit quantization can be used in practical applications to ensure the quality of reconstructed ECG signals, while decrease the bit rate of the data, improving the transmission efficiency, and reduce energy consumption.

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.

SCREENES: Enhancing non-uniform sampling reconstruction for symmetrical NMR spectroscopy

BackgroundSymmetrical NMR spectroscopy, such as Total Correlation Spectroscopy (TOCSY) and other homonuclear spectroscopy, displays symmetry in chemical shift but are generally not symmetrical in terms of intensity, which constitutes a pivotal branch of multidimensional NMR spectroscopy and offers a robust tool for elucidating the structures and dynamics of complex samples, particularly in the context of biological macromolecules. Non-Uniform Sampling (NUS) stands as a critical technique for accelerating multidimensional NMR experiments. However, symmetrical NMR spectroscopy inherently presents dynamic peak intensities, where cross peaks tend to be substantially weaker compared to diagonal peaks. Recovering these weaker cross peaks from NUS data poses a significant challenge, often resulting in compromised data quality. ResultsWe enhance the reconstruction quality of NUS symmetrical NMR spectroscopy based on the assumption that the asymmetry in intensity is mild. Regarding the sampling schedule, we employ the symmetrical sampling structure integrated with Poisson sampling schedule to enhance the efficiency of data acquisition. In term of the reconstruction algorithm, we propose the new method by incorporating hard and soft symmetrical constraints into our recently developed L1-norm-based Compressed Sensing (CS) method known as Sparse Complex-valued REconstruction Enabled by Newton method (SCREEN). Additionally, we propose a two-step reconstruction strategy that separately addresses diagonal and cross peaks. In this two-step strategy, cross peaks are effectively reconstructed by excluding the stronger diagonal peaks. Extensive experimental results validate the effectiveness of our proposed methodology. SignificanceThis method enhances the overall quality of the reconstructed NUS symmetrical NMR spectra, especially in terms of cross peaks, thereby enriching the interpretation of spectral information. Furthermore, it boosts the robustness towards regularization parameters, facilitating a user-friendly experience.

Compressive sensing ISAR imaging with low-rank constraint and anisotropic spatial total variation processing

In order to suppress random noise and remove stripe interference in ISAR imaging, a Compressive Sensing method is proposed for super-resolution ISAR imaging in this paper, which is named LR-ASTV (Low-rank and Anisotropic Spatial Total Variation) algorithm here. In this algorithm, the original echo HRRP is transformed into echo HRRP of MMV model with radial interpolation processing at first. Subsequently, an optimization objective function based on Compressive Sensing framework is formulated which includes the sparsity constraint and low-rank constraint, and this optimization problem is solved by JLRS algorithm to generate an initial ISAR image from which the random noise has been eliminated. The initial image is then subjected to further refinement using the Anisotropic Spatial Total Variation (ASTV) processing, ultimately yielding the final ISAR image with stripe interference removed. To validate the effectiveness of the LR-ASTV algorithm, ISAR imaging experiments based on simulated and measured data at different SNRs are completed, and the imaging results of the LR-ASTV algorithm are compared with those of other three algorithms including the LSM-ME2 algorithm, the JLRS algorithm and the LRPB algorithm. It can be found that the LR-ASTV algorithm has obvious superiority in suppressing random noise and removing stripe interference, and can provide ISAR images of higher clarity. The quality evaluation for ISAR images also shows that the LR-ASTV algorithm has lower image entropy index and higher image contrast index than the other three ISAR imaging algorithms.

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.

A High-Resolution Imaging Method for Multiple-Input Multiple-Output Sonar Based on Deterministic Compressed Sensing.

Differences between conventional sonar and Multiple-Input Multiple-Output (MIMO) sonar systems arise in achieving high angular and range resolution. MIMO sonar uses Matched Filtering (MF) with well-correlated transmitted signals to enhance spatial resolution by obtaining virtual arrays. However, imperfect correlation characteristics yield high sidelobe values, which hinder accurate target localization in underwater imagery. To address this, a Compressed Sensing (CS) method is proposed by reconstructing echo signals to suppress correlation noise between orthogonal waveforms. A shifted dictionary matrix and a deterministic Discrete Fourier Transform (DFT) measurement matrix are used to multiply received echo signals to yield compressed measurements. A sparse recovery algorithm is applied to optimize signal reconstruction before joint transmit-receive beamforming forms a 2D sonar image in the angle-range domain. Numerical simulations and lake experimental results confirm the effectiveness of the proposed method, by obtaining a lower sidelobe sonar image under sub-Nyquist sampling rates as compared with other approaches.

Simulation model of compression of a signal on the basis of the Compressive Sensing method

Detection and recognition of signals in time and frequency domain at different protection of objects and boundaries, carried out on the basis of the geographically distributed systems of protection, is the important task solved with use of sensors on the basis of different the physical principles. Detection and recognition of signals the specified means comes down to processing of big arrays of digital data. Their high-speed performance, energy consumption, mass-dimensional and other characteristics depend on algorithms of processing of these data. In digital signal processing (Digital signal processing DSP) achieved great success in algorithm elaboration for collecting and information extraction from signals. Digitization allowed to create more reliable detection systems and data processings, flexible and cheaper, than analog. At the same time at digital signal processing there is a need of work with more and more high frequencies of sampling, processing, the analysis and storage of large volumes of resultants of data. If the problem of work with high frequencies of sampling could be partially solved at the hardware level using expensive architecture of ATsP consuming high power until recently, then processing and data analysis are even more often carried out on the basis of researches in the field of compression and reduction of dimension of the processed data on the basis of the Compressive Sensing method.

Compressed sensing with log-sum heuristic recover for seismic denoising

The compressed sensing (CS) method, commonly utilized for restructuring sparse signals, has been extensively used to attenuate the random noise in seismic data. An important basis of CS-based methods is the sparsity of sparse coefficients. In this method, the sparse coefficient vector is acquired by minimizing the l1 norm as a substitute for the l0 norm. Many efforts have been made to minimize the lp norm (0 &amp;lt; p &amp;lt; 1) to obtain a more desirable sparse coefficient representation. Despite the improved performance that is achieved by minimizing the lp norm with 0 &amp;lt; p &amp;lt; 1, the related sparse coefficient vector is still suboptimal since the parameter p is greater than 0 rather than infinitely approaching 0 p→0+. Therefore, the CS method with the limit p→0+ is proposed to enhance the sparse performance and thus generate better denoised results in this paper. Our proposed method is referred to as the CS-LHR method because the solving process for minimizing p→0+ is the log-sum heuristic recovery (LHR). Furthermore, to improve the computational efficiency, we incorporate the majorization-minimization (MM) algorithm in this CS-LHR method. Experimental results of synthetic and real seismic records demonstrate the remarkable performance of CS-LHR in random noise suppression.

Low-Cost Quantized Compressed Sensing and Transmission Method for Ultrasonic Imaging Logging

Low-Cost Quantized Compressed Sensing and Transmission Method for Ultrasonic Imaging Logging

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.

Intelligent reconstruction for spatially irregular seismic data by combining compressed sensing with deep learning

Data reconstruction is the most essential step in seismic data processing. Although the compressed sensing (CS) theory breaks through the Nyquist sampling theorem, we previously proved that the CS-based reconstruction of spatially irregular seismic data could not fully meet the theoretical requirements, resulting in low reconstruction accuracy. Although deep learning (DL) has great potential in mining features from data and accelerating the process, it faces challenges in earth science such as limited labels and poor generalizability. To improve the generalizability of deep neural network (DNN) in reconstructing seismic data in the actual situation of limited labeling, this paper proposes a method called CSDNN that combines model-driven CS and data-driven DNN to reconstruct the spatially irregular seismic data. By physically constraining neural networks, this method increases the generalizability of the network and improves the insufficient reconstruction caused by the inability to sample randomly in the whole data definition domain. Experiments on the synthetic and field seismic data show that the CSDNN reconstruction method achieves better performance compared with the conventional CS method and DNN method, including those with low sampling rates, which verifies the feasibility, effectiveness and generalizability of this approach.