Compressive Sensing Recovery Research Articles

In-memory analog solution of compressed sensing recovery in one step

Modern analog computing, by gaining momentum from nonvolatile resistive memory devices, deals with matrix computations. In-memory analog computing has been demonstrated for solving some basic but ordinary matrix problems in one step. Among the more complicated matrix problems, compressed sensing (CS) is a prominent example, whose recovery algorithms feature high-order matrix operations and hardware-unfriendly nonlinear functions. In light of the local competitive algorithm (LCA), here, we present a closed-loop, continuous-time resistive memory circuit for solving CS recovery in one step. Recovery of one-dimensional (1D) sparse signal and 2D compressive images has been experimentally demonstrated, showing elapsed times around few microseconds and normalized mean squared errors of 10 −2 . The LCA circuit is one or two orders of magnitude faster than conventional digital approaches. It also substantially outperforms other (electronic or exotically photonic) analog CS recovery methods in terms of speed, energy, and fidelity, thus representing a highly promising technology for real-time CS applications.

Gradient Pursuit Architecture for Reduced Complexity Sparsity Independent CS Recovery

Compressed sensing (CS) tackles the problem of recovering information from measurements acquired at subNyquist rates. Traditional designs based on orthogonal matching pursuit (OMP) are slowed down by its serial nature and high iteration count in noisy acquisitions. Parallel pursuit strategies in the literature are drawn back by their dependence on sparsity prior and hardware complexity. To address these challenges, an improved version of the sparsity independent regularized pursuit (SIRP) algorithm is proposed in this brief that seeks to achieve a better trade-off between hardware resources and recovery speed without significantly impacting reconstruction quality. A pipelined gradient descent inspired least-mean-squares (LMS) architecture is proposed to replace the complex least squares (LS) step in SIRP and incorporates hardware-sharing for the interdependent steps of the algorithm. The proposed design implemented on a Xilinx Virtex Ultrascale device clocks at 143 MHz and reconstructs a 36-sparse signal in <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$185~\mu \text{s}$ </tex-math></inline-formula> which is competitive with state-of-art designs, at significantly lower hardware consumption. Also, an alternate row LMS scheme is introduced in the design requiring no additional hardware resources, reducing the cycles per iteration to improve reconstruction speed by 28% with a slight reduction in the reconstructed signal-to-noise ratio (RSNR) compared to the full row LMS update.

Sparse Reconstruction Using Hyperbolic Tangent as Smooth l1-Norm Approximation

In the Compressed Sensing (CS) framework, the underdetermined system of linear equation (USLE) can have infinitely many possible solutions. However, we intend to find the sparsest possible solution, which is l0-norm minimization. However, finding an l0 norm solution out of infinitely many possible solutions is NP-hard problem that becomes non-convex optimization problem. It has been a practically proven fact that l0 norm penalty can be adequately estimated by l1 norm, which recasts a non-convex minimization problem to a convex problem. However, l1 norm non-differentiable and gradient-based minimization algorithms are not applicable, due to this very reason there is a need to approximate l1 norm by its smooth approximation. Iterative shrinkage algorithms provide an efficient method to numerically minimize l1-regularized least square optimization problem. These algorithms are required to induce sparsity in their solutions to meet the CS recovery requirement. In this research article, we have developed a novel recovery method that uses hyperbolic tangent function to recover undersampled signal/images in CS framework. In our work, l1 norm and soft thresholding are both approximated with the hyperbolic tangent functions. We have also proposed the criteria to tune optimization parameters to get optimal results. The error bounds for the proposed l1 norm approximation are evaluated. To evaluate performance of our proposed method, we have utilized a dataset comprised of 1-D sparse signal, compressively sampled MR image and cardiac cine MRI. The MRI is an important imaging modality for assessing cardiac vascular function. It provides the ejection fraction and cardiac output of the heart. However, this advantage comes at the cost of a slow acquisition process. Hence, it is essential to speed up the acquisition process to take the full benefits of cardiac cine MRI. Numerical results based on performance metrics, such as Structural Similarity (SSIM), Peak Signal to Noise Ratio (PSNR) and Root Mean Square Error (RMSE) show that the proposed tangent hyperbolic based CS recovery offers a much better performance as compared to the traditional Iterative Soft Thresholding (IST) recovery methods.

Improved Image Compressive Sensing Recovery with Low-Rank Prior and Deep Image Prior

Compressive sensing (CS) aims to recover images with rich and accurate information from a small amount of sampled data. Due to its ill-posedness, the model-based CS method has been widely used ever. In recent years, with the development of the arisen learning-based method, enormous progress has been made in combining learning-based strategy with traditional methods. However, at a low sampling ratio, most such methods tend to over-suppress image information, making the recovered results less satisfactory. In order to push the limits of image CS recovery, we propose a novel non-convex low-rank(NCLR) prior by utilizing weighted Schatten p-norm as a surrogate function of the rank function in low-rank approximation. We then provide a new NCLR-based CS model for image CS recovery by plugging the deep prior as a modular part. In addition, we present an efficient iterated algorithm to solve the proposed model by using the alternating direction method of multiplier (ADMM). Further, the convergence of the proposed method is also illustrated. Extensive experimental results demonstrate that our method achieves good performance in both quantity evaluation and visual perception compared to the existing image CS recovery methods, especially at a low sampling ratio.

Compressive sensing-based channel estimation for high mobile systems with delay Doppler effects

In this paper, channel overhead is reduced by exploiting channel sparsity for multiple input multiple output-orthogonal frequency division multiplexing (MIMO-OFDM) system. Where, compressive sensing (CS) based dictionary design algorithms has been adopted as a channel estimation technique in high mobile systems with minimal number of pilots, such as high-speed train (HST) systems. A novel framework design of the dictionary-based CS was proposed considering both delay and Doppler effects in order to correctly recover the channel response. The channel under consideration is a 2 by 2 space-time block code (STBC) MIMO channel. Simulation tests according to the international telecommunication union (ITU) channel model demonstrated the suitability of the proposed dictionary for estimating the channel impulse response (CIR) of a liner time varying (LTV) channel with a mobility approaches 675 Km/h related to a Doppler frequency of 1500 Hz and 2.4 GHz carrier frequency. Two CS recovery algorithms were applied; orthogonal matching pursuit (OMP) and basis pursuit (BP), where by about 7 dB gain in signal to noise ratio (SNR) was achieved with mobility of 675 Km/h using OMP as compared to BP at a bit error rate (BER) of with 128 OFDM subcarriers.

Distributed ranking-based resource allocation for sporadic M2M communication

This work proposes a novel scheme for distributed ranking-based and contention-free resource allocation in large-scale machine-to-machine (M2M) communication networks. We partition a network of N devices into disjoint clusters based on service type, and assign to each cluster a cluster-specific signature for active cluster members to indicate their active status. The devices in each cluster are totally ordered in some a priori-known manner, which gives rise to an active ranking of active cluster members. In order to tackle complexity issues in large-scale M2M networks with a massive number of devices, we propose a distributed resource allocation scheme using the framework of compressed sensing (CS), which mainly consists of three phases: (i) In a full-duplex acquisition phase, the devices transmit their cluster-specific signatures simultaneously and the network activation pattern is collected in a distributed manner. (ii) The base station detects the active clusters and the number of active devices per cluster using block sketching, and allocates resources to each active cluster accordingly. (iii) Each active device determines its active ranking in the cluster and accesses a specific resource according to the ranking position. By exploiting the sparsity in the activation pattern of the M2M devices, the proposed scheme is formulated as a CS support recovery problem for a particular binary block-sparse signal xin {mathbb{B}}^N – with block sparsity K_{B} and in-block sparsity K_{I} over block size d. Our analysis shows that the proposed scheme efficiently reduces the signature length to mathcal {O}(max {K_{B}log N, K_{B}K_{I}log d}) and achieves less computational complexity of mathcal {O}(dK_{I}^{2}+frac{N}{d}log N) compared with standard CS algorithms. Moreover, numerical results suggest strong robustness of the proposed scheme under noisy conditions.

Cloud-Assisted Image Double Protection System With Encryption and Data Hiding Based on Compressive Sensing

In this paper, we propose a compressive sensing(CS)-based scheme that combines encryption and data hiding to provide double protection to the image data in the cloud outsourcing. Different domain techniques are integrated for efficiency and security. After the data holder gets the sample of the raw data, he embeds watermark into sample and encrypts it, and then sends the protected sample to cloud for storage and recovery. Cloud cannot get any information about either the original data or watermark in the CS recovery process. Finally, users can extract the watermark and decrypt the data recovered by cloud directly in sparse domain. At the same time, after extracting the watermark, the image data of user will be closer to the original data compared with the data without extraction. Besides, the counter (CTR) mode is introduced to generate the measurement matrix of CS, which can improve security while avoiding the storage of measurement matrixes. The experimental results demonstrate that the scheme can provide both privacy protection and copyright protection with high efficiency.

MIMO Radar Imaging Based on Two-dimensional Compressive Sensing Recovery Algorithm

Conventional sparse signal recovery-based MIMO radar imaging method rearranges the received two-dimensional (2D) signals into a vector, However, transforming the two dimensional equation to one dimensional equation then solving linear equation based sparse signal recovery problem requires huge memory and computational budget. A two-dimensional compressed sensing MIMO radar imaging algorithm based on improved smooth L0 norm is proposed in this paper. Firstly, a two-dimensional MIMO radar imaging model is established to transform the imaging problem into a sparse optimization problem. Then, the two-dimensional negative exponential function sequence is used as the smoothed function sequence to approximate the L0 norm. The two-dimensional imaging of MIMO radar is realized by cyclic iteration and gradient projection algorithm. Simulation results show that the proposed algorithm has advantages over the traditional compressed sensing algorithms.

FPGA Implementation of Sparsity Independent Regularized Pursuit for Fast CS Reconstruction

Sparse recovery algorithms are integral to compressed sensing (CS) as they facilitate the reconstruction of higher dimensional signals from sub-Nyquist measurements. Although Orthogonal Matching Pursuit (OMP) has been ubiquitously adopted in hardware implementations to curb the computational complexity of CS recovery, increasing sparsity levels incur higher reconstruction costs. Sparsity independent regularized pursuit (SIRP) is a recent algorithm that employs parallel index selection and regularization to curtail the number of iterations required to reconstruct the signal and thereby enhance the reconstruction speed. This paper proposes a novel reformulation of the SIRP algorithm from the hardware perspective, incorporating a cheaper regularization strategy and a modified Gram-Schmidt (MGS) based incremental QR decomposition (QRD) approach. The proposed design incorporates an iterative QRD architecture with feedback circuitry to exploit the parallelism of the triangularization step in MGS. Additionally, a fast inverse square block circumvents the need for parallel divider blocks giving considerable hardware and latency savings. The design reuses the iterative QRD block to implement the interdependent computations of the algorithm by sophisticated scheduling techniques. The proposed implementation on a Xilinx Virtex Ultrascale FPGA can recover 1024-dimensional signals from 25% measurements within <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$77~\mu \text{s}$ </tex-math></inline-formula> , which translates to a 37% reduction in processing cycles from state-of-art.

Data Traffic Reduction with Compressed Sensing in an AIoT System

To provide Artificial Intelligence (AI) services such as object detection, Internet of Things (IoT) sensor devices should be able to send a large amount of data such as images and videos. However, this inevitably causes IoT networks to be severely overloaded. In this paper, therefore, we propose a novel oneM2M-compliant Artificial Intelligence of Things (AIoT) system for reducing overall data traffic and offering object detection. It consists of some IoT sensor devices with random sampling functions controlled by a compressed sensing (CS) rate, an IoT edge gateway with CS recovery and domain transform functions related to compressed sensing, and a YOLOv5 deep learning function for object detection, and an IoT server. By analyzing the effects of compressed sensing on data traffic reduction in terms of data rate per IoT sensor device, we showed that the proposed AIoT system can reduce the overall data traffic by changing compressed sensing rates of random sampling functions in IoT sensor devices. In addition, we analyzed the effects of the compressed sensing on YOLOv5 object detection in terms of performance metrics such as recall, precision, mAP50, and mAP, and found that recall slightly decreases but precision remains almost constant even though the compressed sensing rate decreases and that mAP50 and mAP are gradually degraded according to the decreased compressed sensing rate. Consequently, if proper compressed sensing rates are chosen, the proposed AIoT system will reduce the overall data traffic without significant performance degradation of YOLOv5.

Dynamic Compressive Data Gathering using Angle-based Random Walk in Hybrid WSNs

This paper addresses the problems of energy consumption, load-balancing, and Compressive Sensing (CS) recovery performance in hybrid proactive-reactive wireless sensor network, where sensors are categorized into two representative and relay nodes. We jointly consider the dynamic compressive data gathering, angle-based random walk, and spatial correlation to propose an efficient method named “Dynamic Compressive Data Gathering using Angle-based Random Walk (DCDG-ARW)”. The proposed scheme uses the CS theory along with the angle-based random walks to transmit CS measurements from sensors to the sink node. To select a starting node for each random walk path, a heuristic mechanism called Distance-and Correlation-aware Node Selection (DCNS) is presented. Furthermore, a transition probability is defined for the proposed angle-based random walks to jointly investigate dynamic changes of the network, increasing load-balancing, and improving the quality of the measurement matrix. The effectiveness of DCDG-ARW is evaluated in terms of energy consumption, load variance, network’s lifetime, and reconstruction error. Based on the simulation results, the proposed DCDG-ARW algorithm illustrates significant performance improvements in comparison to its counterparts across all the aforementioned aspects.

Improved Image Compressive Sensing Recovery with Low-Rank Prior and Deep Image Prior

Improved Image Compressive Sensing Recovery with Low-Rank Prior and Deep Image Prior

Adaptive Under-Sampling Deep Neural Network for Rapid and Reliable Image Recovery in Confocal Laser Scanning Microscope Measurements

Confocal laser scanning microscopy (CLSM) is a non-destructive optical measurement system of high precision, applicable to the construction of three-dimensional (3-D) topographies of biological cells and engineered materials at the micro- and sub-micro scales. Compressive sensing (CS) has recently been applied in microscope systems to reduce the amount of sampled data required for the reconstruction of images; however, the iterative nature of the CS recovery algorithm imposes high computational complexity. This article presents an end-to-end non-iterative deep residual convolutional neural network (CNN) applicable to CLSM systems for CS-based reconstruction. In experiments and numerical simulations, the proposed scheme outperformed the existing CS recovery algorithms in terms of reconstructed image quality and computation time. The proposed algorithm also enabled the reconstruction of images using samples obtained in different regions of an image at various sampling rates to overcome nonuniform information density. The reconstruction performance of the model in terms of robustness and efficiency was validated using real-world CLSM data obtained via random scanning patterns.

Distributed and Cooperative Compressive Sensing Recovery Algorithm for Wireless Sensor Networks with Bi-directional Incremental Topology

Distributed and Cooperative Compressive Sensing Recovery Algorithm for Wireless Sensor Networks with Bi-directional Incremental Topology

Proximal-Gen for fast compressed sensing recovery

Compressed sensing (CS) can recover an image from a few random measurements by exploiting the sparsity assumption on the structure of images. Some recent generative model-based CS recovery methods have removed the sparsity constraint, but their recovery process is slow and the recovered signal is constrained to be in the generator range. Here, we propose a new framework, called Proximal-Gen, for CS recovery. Specifically, we first formulate a general domain of the recovered signals, this allows the subsequent recovery algorithms to recover the signals that deviate from the generator range. Then based on the general domain, we develop a fast recovery algorithm, which mainly consists of two sub-algorithms, namely network-based projected gradient descent (NPGD) and denoiser-based proximal gradient descent (DPGD). The NPGD is used to obtain an intermediate signal lying in the generator range, while the DPGD is proposed to recover a deviation signal. Compared with multiple recent generative model-based recovery methods, our method can achieve better reconstruction performance and higher efficiency under most measurements.

Image Super-Resolution Through Compressive Sensing-based Recovery.

The primary aim of image super-resolution techniques is to produce a high resolution (HR) image from a low resolution (LR) image efficiently. Deep learning algorithms are being extensively used to address the ill-posed problem of single image super-resolution which requires extremely large data-sets and high processing power. When one does not have access to large data-sets or have limited processing power, an alternative technique may be in order. In this study, we have developed a novel positive scale image resizing method inspired by compressive sensing (CS). We have considered the image super-resolution as a CS recovery problem in which a low resolution image is assumed as a compressed measurement and the required interpolated image is treated as output of the CS-based recovery. In the proposed HR recovery method, a deterministic binary block diagonal measurement matrix, (DBBD), is used as measurement matrix since it maintains the visual similarity between the low and high resolution images. Then along with a sparsification matrix, the sparse representation of HR image is first recovered and subsequently the dense HR image is obtained. The proposed method is applied to medical and non-medical images. The HR images obtained using the traditional proximal, bilinear and bi-cubic interpolation techniques are compared with those obtained using the proposed method. The proposed CS inspired method delivers superior HR images than the traditional techniques. The superiority of the proposed method is attributed to the unique usage of the DBBD matrix and the CS recovery algorithm to obtain a high resolution image without any prior training data-set.

Millimeter Wave MIMO out Door Channel Estimation and Precoding

Millimeter wave (mm Wave) communications is one of the technologies for 5G cellular systems. In the mm Wave communication, there is a lot of path loss can be reduced by Precoding. The channel state information (CSI) should be known at the transmitting station, in the design of precoding matrices and to get good accuracy in estimating sparse channels a Compressive sensing (CS) based recovery algorithms was used. Not only for good accuracy the algorithm is also used for mm Wave channel estimation for exploiting the mm Wave channel’s sparse in multi-path construction. Hence, in this paper, for mm Wave outdoor channel estimation, the CS recovery methods orthogonal matching pursuit (OMP) and compressive sampling matching pursuit (CoSaMP) are used. The singular value decomposition (SVD) precoding is developed using the estimated channel. By (MSE) mean square error and spectral efficiency which were the performance metrics in channel estimation and precoding were done by using MATLAB simulations to get the efficacy of the OMP and CoSaMP algorithm.

Truncated tensor-based Bayesian recovery for multidimensional compressive sensing

Bayesian methods are widely used to recover sparse signals from their incomplete measurements with Gaussian white noise. However, while recovering multidimensional signals, these methods are limited by their considerable computational complexities. To address this problem, we develop the truncated Bayesian recovery algorithm for compressive sensing (CS) of multidimensional signals, such as hyperspectral remote sensing images. For each dimension of multidimensional sparse signal, the entries are modeled by the type-II Laplacian prior, such that the support is indicated by the largest variance hyperparameters. The entries of noise tensor are assumed to be independent and Gaussian with zero mean. We approximately estimate the hyperparameters using the maximum a posteriori (MAP) process to determine the supports for each dimension. Based on the supports, the recovered sparse signal is obtained through the tensor-based least square strategy. The required number of iterative cycles can be significantly reduced, compared with conventional method that iterates the MAP process until convergence. Experimental results on synthetic data, hyperspectral images, and hyperspectral remote sensing images demonstrate that the proposed algorithm can obviously speed up multidimensional Bayesian CS recovery.

A Compressed Sensing Recovery Algorithm Based on Support Set Selection

The theory of compressed sensing (CS) has shown tremendous potential in many fields, especially in the signal processing area, due to its utility in recovering unknown signals with far lower sampling rates than the Nyquist frequency. In this paper, we present a novel, optimized recovery algorithm named supp-BPDN. The proposed algorithm executes a step of selecting and recording the support set of original signals before using the traditional recovery algorithm mostly used in signal processing called basis pursuit denoising (BPDN). We proved mathematically that even in a noise-affected CS system, the probability of selecting the support set of signals still approaches 1, which means supp-BPDN can maintain good performance in systems in which noise exists. Recovery results are demonstrated to verify the effectiveness and superiority of supp-BPDN. Besides, we set up a photonic-enabled CS system realizing the reconstruction of a two-tone signal with a peak frequency of 350 MHz through a 200 MHz analog-to-digital converter (ADC) and a signal with a peak frequency of 1 GHz by a 500 MHz ADC. Similarly, supp-BPDN showed better reconstruction results than BPDN.

Sensor position optimization for flux mapping in a nuclear reactor using compressed sensing

The paper presents a novel approach to sensor position optimisation based on compressed sensing (CS) and its application to neutron flux estimation in a nuclear reactor. An online flux mapping system (FMS) with a suitable algorithm is needed to continuously monitor neutron flux distribution from the measurements of in-core detectors in large nuclear reactors. In the present work, sensor positions are optimized by designing a sensing matrix Φ for the CS system in which the dictionary is known in advance. The sensing matrix is optimized by maximising the incoherence of the dictionary matrix and incorporating the estimation error in the optimization process. The proposed method uses the CS recovery technique, Basis Pursuit De-Noising (BPDN), for flux mapping along the vertical direction at the detector housing locations (1-D). In the end, the method suggests the optimized positions and number of sensors for efficient estimation of neutron flux inside the reactor core.