Compressed Sensing Recovery Methods 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.

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.

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.

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.

Group Sparsity Residual Constraint with Non-Local Priors for Image Restoration.

Group sparse representation (GSR) has made great strides in image restoration producing superior performance, realized through employing a powerful mechanism to integrate the local sparsity and nonlocal self-similarity of images. However, due to some form of degradation (e.g., noise, down-sampling or pixels missing), traditional GSR models may fail to faithfully estimate sparsity of each group in an image, thus resulting in a distorted reconstruction of the original image. This motivates us to design a simple yet effective model that aims to address the above mentioned problem. Specifically, we propose group sparsity residual constraint with nonlocal priors (GSRC-NLP) for image restoration. Through introducing the group sparsity residual constraint, the problem of image restoration is further defined and simplified through attempts at reducing the group sparsity residual. Towards this end, we first obtain a good estimation of the group sparse coefficient of each original image group by exploiting the image nonlocal self-similarity (NSS) prior along with self-supervised learning scheme, and then the group sparse coefficient of the corresponding degraded image group is enforced to approximate the estimation. To make the proposed scheme tractable and robust, two algorithms, i.e., iterative shrinkage/thresholding (IST) and alternating direction method of multipliers (ADMM), are employed to solve the proposed optimization problems for different image restoration tasks. Experimental results on image denoising, image inpainting and image compressive sensing (CS) recovery, demonstrate that the proposed GSRC-NLP based image restoration algorithm is comparable to state-of-the-art denoising methods and outperforms several state-of-the-art image inpainting and image CS recovery methods in terms of both objective and perceptual quality metrics.

Toward Theoretically Founded Learning-Based Compressed Sensing

Noiseless compressed sensing refers to the problem of recovering a (high-dimensional) signal from its under-determined linear measurements. For compressed sensing to be feasible, the signal needs to be structured. While the main focus of the field has been on simple structures such as sparsity, there has been a growing interest in moving beyond sparsity and having a comprehensive compressed sensing framework that covers general structures. Two recent approaches that aim at developing such a framework from different perspectives are i) Quantized maximum a posteriori (Q-MAP), a Bayesian method that assumes full knowledge of the source distribution, and ii) Lagrangian minimum entropy pursuit (L-MEP), a universal recovery method that requires no prior knowledge about the distribution of the source. In this paper, by establishing theoretical connections between L-MEP and Q-MAP, it is shown how the two methods are complementary to each other and lead to a theoretically-founded learning-based recovery method that applies to sources with general structures. Unlike a Bayesian or a universal method, a learning-based method is able to extract the source structure from training data. The effect of error in estimating the source structure on the performance of the learning-based compressed sensing recovery method is characterized.

Formula omitted] norm regularization based group sparse representation for image compressed sensing recovery

One important challenge in image compressed sensing (CS) recovery methods is to develop a sparsity inducing model which can reflect the image priors appropriately and hence yields high quality recovery results. Recent advances have suggested that group sparse representation based models, which exploit nonlocal self-similarity prior, lead to superior results in image CS recovery. In this paper, we propose a CS recovery method via group sparse representation with nonconvex LLp norm regularization (GSR-LLp). In the proposed method, nonconvex LLp norm with (0<p≤1) is introduced as a new sparsity metric to better promote the sparsity of the group coefficients, rather than the l0 norm. Furthermore, the principle component analysis (PCA) is utilized to learn an adaptive orthogonal dictionary for each group. To solve the GSR-driven LLp minimization problem, an efficient algorithm based on split Bregman framework and Majorization–Minimization (MM) algorithm is developed. Moreover, the proposed model is combined with a robust M-estimate to cope with the case where measurements are corrupted by impulsive noise. In this case, we substitute the l2 norm data fidelity with Welch m-estimate which has shown the advantage of robustness against heavy-tailed impulsive noise. We develop an efficient scheme based on split Bregman framework and half-quadratic (HQ) theory to solve the resulting optimization problem (called as RGSR-LLp). Extensive experimental results show effectiveness of the proposed methods compared with the state-of-the-arts methods in CS image recovery.

Image compressed sensing recovery via nonconvex garrote regularization

Sparsity inducing model is one of the most important components of image compressed sensing (CS) recovery methods. These models are built on the image prior knowledge. The model which can reflect the image priors appropriately, yields high quality recovery results. Recent studies have shown that nonlocal low-rank prior based models often lead to superior results in CS recovery. The rank regularization problem resulting from these models is an NP-hard problem and how to solve it has a great impact on the recovery results. In this paper, we propose a new CS recovery method via nonconvex Garrote regularization (NGR) toward better exploiting the nonlocal low-rank prior. In the proposed CS-NGR method, the nonconvex Garrote function is introduced as a suitable surrogate for the rank function. To solve the resulting minimization problem efficiently, we employ the alternating direction method and so-called Garrote singular value shrinkage (GSVS) technique. Extensive experimental results show effectiveness of the proposed method compared with the state-of-the-arts methods in CS image recovery.

A Data Loss Recovery Technique using Compressive Sensing for Structural Health Monitoring Applications

Recent developments in Wireless Sensor Networks (WSN) benefited various fields, among them Structural Health Monitoring (SHM) is an important application of WSNs. Using WSNs provides multiple advantages such as continuous monitoring of structure, lesser installation costs, fewer human inspections. However, because of the wireless medium, hardware faults, etc., data loss is an unavoidable consequence of WSNs. Recently, a new class of data loss recovery technique using Compressive Sensing (CS) is getting attention from the research community. In these methods, the transmitter sends encoded acceleration data and receiver uses a CS recovery method to recover the original signal. Usually, the encoding process uses a random measurement matrix which makes the process computationally complex to implement on sensor nodes. This paper presents a technique where the signal is encoded using Scrambled Identity Matrix. Using this method reduces the computational complexity and also robust to data loss. A performance analysis of the proposed technique is presented for random and continuous data loss. A comparison with the existing data loss recovery techniques is also shown using simulated data loss (both random and continuous data loss). It is observed that the proposed technique using Scrambled Identity Matrix can reconstruct the signals even after significant loss of data.

Pulsed-high Intensity Focused Ultrasound Therapy of Rabbit Middle Cerebral Artery Thromboembolism Accompanied by Anticoagulant Nanoparticles Administration

One important challenge in image compressed sensing (CS) recovery methods is to develop a sparsity inducing model which can reflect the image priors appropriately and hence yields high quality recovery results. Recent advances have suggested that group sparse representation based models, which exploit nonlocal self-similarity prior, lead to superior results in image CS recovery. In this paper, we propose a CS recovery method via group sparse representation with nonconvex LLp norm regularization (GSR-LLp). In the proposed method, nonconvex LLp norm with (0<p≤1) is introduced as a new sparsity metric to better promote the sparsity of the group coefficients, rather than the l0 norm. Furthermore, the principle component analysis (PCA) is utilized to learn an adaptive orthogonal dictionary for each group. To solve the GSR-driven LLp minimization problem, an efficient algorithm based on split Bregman framework and Majorization–Minimization (MM) algorithm is developed. Moreover, the proposed model is combined with a robust M-estimate to cope with the case where measurements are corrupted by impulsive noise. In this case, we substitute the l2 norm data fidelity with Welch m-estimate which has shown the advantage of robustness against heavy-tailed impulsive noise. We develop an efficient scheme based on split Bregman framework and half-quadratic (HQ) theory to solve the resulting optimization problem (called as RGSR-LLp). Extensive experimental results show effectiveness of the proposed methods compared with the state-of-the-arts methods in CS image recovery.

Hardware Implementation of Iterative Method With Adaptive Thresholding for Random Sampling Recovery of Sparse Signals

Sparse recovery methods find extensive applications in various fields such as image and audio processing, wireless communication, and spectral estimation. In this paper, a hardware architecture of iterative method with adaptive thresholding (IMAT) is presented to recover a sparse signal from its random samples. To demonstrate the effectiveness of IMAT, a comparison is performed between the IMAT algorithm and the compressive sensing recovery method, orthogonal matching pursuit, in terms of complexity and reconstruction quality. In the context of image reconstruction, as a practical case, simulation results show the advantages of IMAT in improving the performance of the signal reconstruction via peak signal-to-noise ratio and structural similarity index metrics. Since IMAT employs discrete transform as a principal operation in each iteration, using fast or fast approximate algorithms allows more efficient implementation. In this paper, two multiplication-free transforms, Walsh–Hadamard transform (WHT) and approximate discrete cosine transform (ADCT), are used to reduce computational complexity of IMAT implementation. The IMAT recovery algorithm is implemented on Virtex6 FPGA using two above transforms, and the results are compared with respect to the hardware resource utilization, power consumption, and recovery time. The results demonstrate that using WHT for IMAT implementation is more efficient than using ADCT in terms of hardware resources. Also, the comparison implies that the performance of the hardware implementation is very close to its floating point simulated counterpart. For a block size of $32 \times 32$ , the IMAT implementation using WHT provides the reconstruction time of $185~\mu \text{s}$ and the dynamic power of 123 mW.

Training-free compressed sensing for wireless neural recording using analysis model and group weighted -minimization

Objective. Data compression is crucial for resource-constrained wireless neural recording applications with limited data bandwidth, and compressed sensing (CS) theory has successfully demonstrated its potential in neural recording applications. In this paper, an analytical, training-free CS recovery method, termed group weighted analysis -minimization (GWALM), is proposed for wireless neural recording. Approach. The GWALM method consists of three parts: (1) the analysis model is adopted to enforce sparsity of the neural signals, therefore overcoming the drawbacks of conventional synthesis models and enhancing the recovery performance. (2) A multi-fractional-order difference matrix is constructed as the analysis operator, thus avoiding the dictionary learning procedure and reducing the need for previously acquired data and computational complexities. (3) By exploiting the statistical properties of the analysis coefficients, a group weighting approach is developed to enhance the performance of analysis -minimization. Main results. Experimental results on synthetic and real datasets reveal that the proposed approach outperforms state-of-the-art CS-based methods in terms of both spike recovery quality and classification accuracy. Significance. Energy and area efficiency of the GWALM make it an ideal candidate for resource-constrained, large scale wireless neural recording applications. The training-free feature of the GWALM further improves its robustness to spike shape variation, thus making it more practical for long term wireless neural recording.

Sparse Signal Aloha: A Compressive Sensing-Based Method for Uncoordinated Multiple Access

We investigate the problem of sparse signal medium access control in the wireless sensor networks. The proposed sparse signal Aloha (SSA) transmits sampled compressive data to the fusion center using Aloha random access protocol. In order to maximize the overall data transmission rate in the presence of packet collision, redundant data are randomly subsampled at individual sensor nodes according to an optimal subsampling rate before transmission. Data loss due to random subsampling and collision in the wireless channel are compensated using compressive sensing recovery method at the fusion center. Simulation results verify the theoretical analysis and show the significant improvement of SSA compared with existing CS-based random access method.

Subband-dependent compressed sensing in local CT reconstruction

To achieve high-quality low-dose computed tomography (CT) images, compressed sensing (CS)-based CT reconstructions recover the images using fewer projections; and wavelet inverse Radon algorithms recover wavelet subbands of CT images from locally scanned projections. Moreover, it has been shown that subband CS algorithms accelerate the convergence of the CS recovery methods. Here, we propose an innovative combination of a newly developed accelerated wavelet inverse Radon transform and non-convex CS formulation to recover the wavelet subbands of CT images from a reduced number of locally scanned X-ray projections. Fast pseudo-polar Fourier transform is used to decrease the computational complexity of CS recovery. Therefore, the proposed method, denoted by AWiR-SISTA, reduces the radiation dose by simultaneously decreasing the X-ray exposure area and the number of projections, decreases the CS computational complexity, and accelerates the CS recovery convergence rate. Phantom-based simulations show that high-quality ultra-low-dose local CT images can be reconstructed using the proposed method in few seconds, without numerical optimization. Clinical chest CT images are used to demonstrate the practical potential of the method.

Sequential Compressed Sensing With Progressive Signal Reconstruction in Wireless Sensor Networks

This paper considers sequential compressed acquisition and progressive reconstruction of spatially and temporally correlated sensor data streams in wireless sensor networks (WSNs) via compressed sensing (CS). We develop a sequential framework based on sliding window processing, in which the sink can efficiently reconstruct the current sensors' readings from a sequence of periodically delivered CS measurements by exploiting the joint compressibility via Kronecker sparsifying bases. Specifically, we derive a recursive CS recovery method which utilizes the estimates from the preceding decoding instants via a regularization and reweighted ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> -minimization to improve the reconstruction accuracy of sensor data streams while reducing the necessary communications. As beneficial features, the method produces estimates for the current sensors' readings without additional decoding delay, and, via adjusting the window size, it can dynamically trade-off between the CS recovery performance and decoding complexity. Numerical results show that our proposed method achieves higher reconstruction accuracy with a smaller number of required transmissions, and with lower decoding delay and complexity as compared to those of the state of the art CS methods.

Accurate OFDM Sparse Channel Estimation by Optimal Deterministic Pilot Pattern

ABSTRACTIn orthogonal frequency division multiplexing (OFDM) systems the wireless channel impulse response can be modelled as a sparse vector. Recently emerged compressed sensing (CS) theory can be used for reconstruction and estimation of unknown non-zero channel taps. In CS-based channel estimation, the number of pilot sub-carriers can be decreased, so the spectral efficiency of the system can be increased. The efficiency and performance of sparse channel estimation (SCE) highly depend on the measurement matrix, which in turn depends on the pilot pattern. In this paper, based on minimization of the correlation between all columns of measurement matrix, a new criterion is proposed. In addition, a deterministic pilot pattern optimization algorithm for OFDM SCE is introduced. Greedy CS recovery methods, such as orthogonal matching pursuit (OMP) and regularized OMP are used for estimation of the channel taps. The simulation results confirm the efficiency and accuracy of proposed criterion and optimization algorithm in terms of mean square error.

Compressed Sensing Methods for DNA Microarrays, RNA Interference, and Metagenomics

Compressed sensing (CS) is a sparse signal sampling methodology for efficiently acquiring and reconstructing a signal from relatively few measurements. Recent work shows that CS is well-suited to be applied to problems in genomics, including probe design in microarrays, RNA interference (RNAi), and taxonomic assignment in metagenomics. The principle of using different CS recovery methods in these applications has thus been established, but a comprehensive study of using a wide range of CS methods has not been done. For each of these applications, we apply three hitherto unused CS methods, namely, l1-magic, CoSaMP, and l1-homotopy, in conjunction with CS measurement matrices such as randomly generated CS m matrix, Hamming matrix, and projective geometry-based matrix. We find that, in RNAi, the l1-magic (the standard package for l1 minimization) and l1-homotopy methods show significant reduction in reconstruction error compared to the baseline. In metagenomics, we find that l1-homotopy as well as CoSaMP estimate concentration with significantly reduced time when compared to the GPSR and WGSQuikr methods.

Row-sparse blind compressed sensing for reconstructing multi-channel EEG signals

This communication concentrates on application of blind compressed sensing (BCS) framework for reconstruction of multichannel electroencephalograph (EEG) signal for wireless body area networks (WBANs). Compressed sensing (CS) based techniques employ a known sparsifying basis (wavelet/DCT/Gabor). BCS learns the sparsifying dictionary while recovering the signal. The BCS framework was proposed for recovering sparse signals. A recent work showed that, EEG signals can be better recovered by exploiting inter-channel correlation. This led to a row-sparse recovery problem. In this work, we modify the basic BCS framework for recovering row-sparse signal ensembles – this leads to better EEG reconstruction accuracy compared to prior CS recovery methods. The success of this technique enables reducing the energy expenditure of the sensor nodes of the WBAN.

Sub-Nyquist Radar via Doppler Focusing

We investigate the problem of a monostatic pulse-Doppler radar transceiver trying to detect targets sparsely populated in the radar's unambiguous time-frequency region. Several past works employ compressed sensing (CS) algorithms to this type of problem but either do not address sample rate reduction, impose constraints on the radar transmitter, propose CS recovery methods with prohibitive dictionary size, or perform poorly in noisy conditions. Here, we describe a sub-Nyquist sampling and recovery approach called Doppler focusing, which addresses all of these problems: it performs low rate sampling and digital processing, imposes no restrictions on the transmitter, and uses a CS dictionary with size, which does not increase with increasing number of pulses P. Furthermore, in the presence of noise, Doppler focusing enjoys a signal-to-noise ratio (SNR) improvement, which scales linearly with P, obtaining good detection performance even at SNR as low as - 25 dB. The recovery is based on the Xampling framework, which allows reduction of the number of samples needed to accurately represent the signal, directly in the analog-to-digital conversion process. After sampling, the entire digital recovery process is performed on the low rate samples without having to return to the Nyquist rate. Finally, our approach can be implemented in hardware using a previously suggested Xampling radar prototype.

Fractal pursuit for compressive sensing signal recovery

Basis pursuit (BP) and matching pursuit (MP) are two important basic recovery methods in compressive sensing (CS) research. BP can compute the global optimal solution in CS recovery problem, but its computational complexity is high and dimensional universality (regardless of 1D or 2D or higher dimensions) is not good. On the other side, the computational cost of MP is lower than BP, but the sparsity of signal needs to be known beforehand and its solution may not necessarily be global optimal. In this paper, a new CS recovery method is proposed, termed fractal pursuit (FP) which integrates the advantage of BP and MP. It acquires the prior knowledge of signal by fractal recognition to cut down the computational cost of pursuit operation, and uses fractal minimization in place of l1-norm minimization for improving the recovery quality and dimensional universality in CS framework. Two experiments show the feasibility and performance of FP in CS recovery.