Compressive Sensing Recovery Algorithms Research Articles

SCWOMP Recovery Algorithm for 5G MIMO Communication Symbol Detection

In order to solve the problem of small capacity and high energy consumption in China’s 5G communication technology system, the research proposes that based on the segmented weakly orthogonal matching pursuit (SWOMP) algorithm, it is combined with the compressed sensing matching pursuit algorithm to form a segmented backtracking weak selection positive algorithm and Cross Match Tracking (SCWOMP) algorithm. First, the sparseness of MIMO system technology and its transmission structure is analyzed. Then, the new model is built after comparing with other algorithms, and the problem of overestimating the low recovery probability in the calculation process is improved by the backtracking of the algorithm and the improvement of the angle of the atomic column selection, so as to reduce the number of iterations and improve the performance of the algorithm. The results show that, in the performance comparison of different sampling points under different compressed sensing recovery algorithms, the recovery probability of the SCWOMP algorithm is the best, and when the number of sampling points is 80, although the fixed step size of the SCWOMP algorithm is different, there is recovery. The probability has a maximum value, close to 1. Then, the improved compressed sensing recovery algorithm is simulated and analyzed. When the pruning coefficient is 0.5 and the number of sampling points is 80, the reconstruction rate has a maximum value, and when other algorithms reach the maximum reconstruction rate, the number of sampling points (M) is significantly greater than that of the SCWOMP algorithm. An increase in the rate of reduction of the reconstruction probability of the SCWOMP algorithm is significantly lower than that of other algorithms; when sparsity is equal to 70, the reconstruction probability becomes 0, indicating that SCWOMP has a wider reconfigurable range and has a significant performance effect. This shows that the proposed SCWOMP algorithm has the best detection performance for 5G communication symbol detection, which can effectively increase the capacity of the system and better promote technology.

Adversarial Autoencoder Empowered Joint Anomaly Detection and Signal Reconstruction From Sub-Nyquist Samples

Anomaly detection is an essential part of spectrum monitoring applications. Malicious users and malfunctioning nodes could be identified via anomaly detection methods. Meanwhile, the spectrum bands that would be utilized in future 6G or satellite communication system settings are going to be wider than ever. Acquiring Nyquist sampled data from such a spectrum would require components with a very high sampling rate. To monitor a wide spectrum, a compressive sensing recovery algorithm combined with a sub-sampling approach could accomplish the task with a lower hardware cost. To solve the anomaly detection problem using a sub-sampled data stream, a joint signal recovery and anomaly detection solution utilizing an adversarial autoencoder (AAE) structure are proposed in this article. An AAE is constructed via an autoencoder and a discriminator weaved together. The discriminator would guide the autoencoder to drive its extracted feature onto a designed feature space, while the autoencoder would provide a reconstruction of the original Nyquist sampled signal. The proposed AAE structure could learn the distribution of the signal from either labelled or unlabelled training data, enabling it to work on both supervised and unsupervised data sets. The proposed AAE has shown superior reconstruction and detection performance on very sparse sampling scenarios.

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.

Performance analysis of compressive sensing recovery algorithms for image processing using block processing

<p>The modern digital world comprises of transmitting media files like image, audio, and video which leads to usage of large memory storage, high data transmission rate, and a lot of sensory devices. Compressive sensing (CS) is a sampling theory that compresses the signal at the time of acquiring it. Compressive sensing samples the signal efficiently below the Nyquist rate to minimize storage and recoveries back the signal significantly minimizing the data rate and few sensors. The proposed paper proceeds with three phases. The first phase describes various measurement matrices like Gaussian matrix, circulant matrix, and special random matrices which are the basic foundation of compressive sensing technique that finds its application in various fields like wireless sensors networks (WSN), internet of things (IoT), video processing, biomedical applications, and many. Finally, the paper analyses the performance of the various reconstruction algorithms of compressive sensing like basis pursuit (BP), compressive sampling matching pursuit (CoSaMP), iteratively reweighted least square (IRLS), iterative hard thresholding (IHT), block processing-based basis pursuit (BP-BP) based onmean square error (MSE), and peak signal to noise ratio (PSNR) and then concludes with future works.</p>

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.

Fully cooperative and distributed focal underdetermined system solver compressive sensing recovery algorithm for wireless sensor networks

SummaryThe designed algorithms for wireless sensor networks (WSNs) should not impose a high computational load on sensor nodes because they are battery‐powered devices. To distribute the computations between sensors, distributed algorithms are required. On the other hand, since the sensors observe related phenomena, the acquired signals, besides the intra‐signal correlation, also have some inter‐signal correlation. When the designed algorithms are cooperative, these joint structures are used. In this study, we propose a distributed and cooperative algorithm based on the focal underdetermined system solver (FOCUSS) for compressive sensing signal reconstruction in WSNs. Unlike the other FOCUSS‐based sparse recovery algorithms, the proposed algorithm is quite distributed and implemented by one‐hop communication between the neighboring node without collaborating any fusion center (FC). In the suggested system model, the reconstructed signals from the underdetermined systems of equations are different for each sensor node. The obtained results verified that the proposed approach performs better than the existing works regarding signal reconstruction and convergence rate.

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.

Mathematical Foundation of Sparsity-Based Multi-Illumination Super-Resolution∗

It is well-known that the resolution of a traditional optical imaging system is limited by the so-called Rayleigh limit, which is of several hundreds of nanometers. By employing fluorescence techniques, modern microscopic methods can resolve point scatterers separated much lower than the Rayleigh limit. Localization-based fluorescence subwavelength imaging techniques such as PALM and STORM can achieve a spatial resolution of several tens of nanometers. However, these techniques have limited temporal resolution as they require tens of thousands of exposures. Employing sparsity-based models and recovery algorithms is a natural way to reduce the number of exposures and hence obtain high temporal resolution. Recently, a new multi-illumination imaging technique called Brownian Excitation Amplitude Modulation microscopy (BEAM) is introduced. BEAM achieves a threefold resolution improvement by applying a compressive sensing recovery algorithm over only few frames. Motivated by BEAM, our aim in this paper is to pioneer the mathematical foundation for sparsity-based multi-illumination super-resolution. We consider several diffraction-limited images from samples exposed to different illumination patterns and recover the source by considering the sparsest solution. We estimate the minimum separation distance between point scatterers so that they could be stably recovered. By this estimation, we reveal the dependence of the resolution on the cut-off frequency of the imaging system, the SNR, the sparsity of point scatterers, and the incoherence of illumination patterns. Our theory particularly highlights the importance of the high incoherence of illumination patterns in enhancing the resolution. It also demonstrates that super-resolution can be achieved using sparsity-based multi-illumination imaging with very few frames, whereby the spatio-temporal super-resolution becomes possible.

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

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.

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.

Split–Process–Merge Technique-Based Algorithm for Accelerated Recovery of Compressively Sensed Images and Videos

Greater compression ratio can be achieved while compressing images and videos by using the technique called compressive sensing or compressed sensing (CS). In CS, sparsity of the signal is exploited in order to achieve high compression. CS-based compression converts the images and video frames to a set of $$m<n$$ measurements, which are transmitted to the receiver where the images and video frames are recovered by an efficient reconstruction algorithm with minimum error. Many reconstruction procedures solve least squares problem iteratively to recover the original signal, which ultimately increases the algorithmic complexity and runtime. In this work, split, process and merge technique for image and video reconstruction is proposed, which surpasses the adversities of the iterative algorithms, and provides better reconstruction performance in terms of perception and objective measures. Even with small number of measurements, the peak to signal noise ratio obtained using split and merge technique is above 30 dB, and the structural similarity is above 97% with an accuracy of 98% for both images and videos. The total runtime of the proposed algorithm is around 1.5 s and 9 s for images and videos respectively, which is small compared to iterative algorithms. Thus, the proposed split and merge technique based compressive sensing recovery algorithm proves to perform better in terms of speed and reconstruction quality.

Single photon counting compressive imaging using a generative model optimized via sampling and transfer learning.

Single photon counting compressive imaging, a combination of single-pixel-imaging and single-photon-counting technology, is provided with low cost and ultra-high sensitivity. However, it requires a long imaging time when applying traditional compressed sensing (CS) reconstruction algorithms. A deep-learning-based compressed reconstruction network refrains iterative computation while achieving efficient reconstruction. This paper proposes a compressed reconstruction network (OGTM) based on a generative model, adding sampling sub-network to achieve joint-optimization of sampling and generation for better reconstruction. To avoid the slow convergence caused by alternating training, initial weights of the sampling and generation sub-network are transferred from an autoencoder. The results indicate that the convergence speed and imaging quality are significantly improved. The OGTM validated on a single-photon compressive imaging system performs imaging experiments on specific and generalized targets. For specific targets, the results demonstrate that OGTM can quickly generate images from few measurements, and its reconstruction is better than the existing compressed sensing recovery algorithms, compensating defects of the generative models in compressed sensing.

Design and Application of a Greedy Pursuit Algorithm Adapted to Overcomplete Dictionary for Sparse Signal Recovery

Compressive sensing (CS) is a novel paradigm to recover a sparse signal in compressed domain. In some overcomplete dictionaries, most practical signals are sparse rather than orthonormal. Signal space greedy method can derive the optimal or near-optimal projections, making it possible to identify a few most relevant dictionary atoms of an arbitrary signal. More practically, such projections can be processed by standard CS recovery algorithms. This paper proposes a signal space subspace pursuit (SSSP) method to compute spare signal representations with overcomplete dictionaries, whenever the sensing matrix satisfies the restricted isometry property adapted to dictionary (D-RIP). Specifically, theoretical guarantees were provided to recover the signals from their measurements with overwhelming probability, as long as the sensing matrix satisfies the D-RIP. In addition, a thorough analysis was performed to minimize the number of measurements required for such guarantees. Simulation results demonstrate the validity of our hypothetical theory, as well as the superiority of the proposed approach.

Toward Efficient Compressed-Sensing-Based RFID Identification: A Sparsity-Controlled Approach

Radio-frequency identification (RFID) has pervasive applications in building ultralow-power ubiquitous networks, where backscatter communication during tag identification is neither reliable nor efficient. Inspired by the sparsity that only a few RFID tags communicate with the reader simultaneously, many compressed sensing (CS)-based schemes have been proposed to exploit the colliding tag responses to facilitate efficient tag identification. However, most of them suffer from huge ID search space and signature collision during the CS recovery process. To address these issues, we propose SCRIC, a novel sparsity-controlled RFID identification scheme using a random signature assignment, which achieves a faster and more robust identification performance. Specifically, to tackle identification failure caused by severe signature collision, we assign each active tag an access probability to control the sparsity and reduce signature collision. Theoretical analysis is given to prove that the signature collision probability of the proposed scheme is reduced compared with the existing random signature scheme and an optimal access probability is derived. Moreover, considering that conventional CS recovery algorithm relies heavily on the unpractical assumption that the active tag number is known precisely in advance, we integrate the cross validation (CV) into CS recovery algorithms and propose a greedy algorithm called the CV-based orthogonal matching pursuit (OMP-CV), which can reduce the tag identification false alarm rate without any prior knowledge. Extensive experimental results show that the proposed mechanism significantly outperforms the existing CS-based tag identification methods in terms of identification speed and robustness to noise.

Detection Algorithm of Compressed Sensing Signal in Generalized Spatial Modulation System

For the generalized spatial modulation in the underdetermined system with the number of transmitting antennas larger than the number of receiving antennas, the activation of the antenna is small and inaccurate. The traditional MMSE algorithm and the ZF algorithm still perform the pseudo-inverse operation on the entire channel matrix, which results in a large number of redundancy. Although the ML algorithm has the best detection performance, the complexity is difficult to meet the actual requirements. In this paper, for the sparse characteristics of generalized spatial modulation signals, a detection algorithm is improved based on the compressed sensing recovery algorithm SWOMP. The algorithm first selects multiple or one active antenna sequences conforming to the spatial modulation to form an index set according to the situation, and then uses the backtracking principle to select the atomic column according to the threshold, rejects the unreliable sequence, and finally uses the minimum mean square error algorithm to detect the modulation symbol according to the activated antenna index. The pseudo-inverse operation of the entire channel matrix is avoided, and the bit error rate is lower than the ZF algorithm, the MMSE algorithm and the OMP algorithm, and the performance of the proposed algorithm is closer to the ML algorithm, which is a better way that balance between complexity and detection performance.

Expectation maximization identification algorithm for time-delay two-dimensional systems

In time-delay two-dimensional (2-D) systems, the variables not only depend on time but also on spatial coordinates, moreover, more than one input data are subjected to time-delays at each sampling time. In order to overcome these difficulties, this paper develops an expectation maximization (EM) identification algorithm for estimating the 2-D systems. Compared with the traditional compressed sensing recovery algorithm and the redundant rule based estimation algorithm, the EM algorithm in this paper has three integrated key functions, (1) to estimate the parameters and the unknown time-delays simultaneously, (2) to keep the number of the unknown parameters unchanged, (3) to identify the 2-D systems with varying time-delays. The simulations made further guarantees the usefulness of the proposed algorithm.

COMPRESSIVE SENSING IN QUADRATURE FREQUENCY MODULATED THERMAL WAVE IMAGING

Active thermography uses IR camera to capture the thermal response from a test sample to detect defects in the materials. Depending on the material geometry, externally Quadrature Frequency Modulated (QFM) optical stimulation consisting of very low frequency components usually less than 1 HZ is projected on the test sample. IR camera captures the thermal response from test material at a frequency much higher than the required nyquist rate. This is wastage of resources such as sensors, memory and power. In this paper Compressive Sensing (CS) is used to capture the thermal response from aluminum and bone test samples using IR camera at a reduced frame rate and then complete response is recovered using CS recovery algorithms Basis Pursuit (BP) and Orthogonal Matching Pursuit (OMP). Recovered thermal response is processed using correlation based pulse compression approach to perform subsurface analysis to detect the defects. To verify the effectiveness of the recovery algorithms comparison is done between original and recovered data and the results are promising.

Incremental and diffusion compressive sensing strategies over distributed networks

Compressive sensing (CS) has been widely used in wireless sensor networks (WSNs). In WSNs, the sensors are battery-powered and hence their communication and processing powers are limited. One of the dominant features of the CS is its complex recovery phase. Thus, great care should be taken into account when designing the CS recovery algorithm for WSNs. In this paper, we propose a distributed and cooperative recovery algorithm for two different cooperation modes of sensor networks including incremental and diffusion. The theoretical performance analysis of the proposed algorithms in both exact and noisy measurements is investigated. The obtained results show the superiority of the proposed method in terms of convergence rate and steady-state error compared with the non-cooperative scenario and the well-known distributed least absolute shrinkage and selection operator (D-LASSO) approach. Furthermore, the proposed structure requires much fewer measurements for exact recovery.

Multi-Channel Deep Networks for Block-Based Image Compressive Sensing

Incorporating deep neural networks in image compressive sensing (CS) receives intensive attentions in multimedia technology and applications recently. As deep network approaches learn the inverse mapping directly from the CS measurements, the reconstruction speed is significantly faster than the conventional CS algorithms. However, for existing network based approaches, a CS sampling procedure has to map a separate network model. This may potentially degrade the performance of image CS with block-wise sampling because of blocking artifacts, especially when multiple sampling rates are assigned to different blocks within an image. In this paper, we develop a multichannel deep network for block-based image CS by exploiting inter-block correlation with performance significantly exceeding the current state-of-the-art methods. The significant performance improvement is attributed to block-wise approximation but full image removal of blocking artifacts. Specifically, with our multichannel structure, the image blocks with a variety of sampling rates can be reconstructed in a single model. The initially reconstructed blocks are then capable of being reassembled into a full image to improve the recovered images by unrolling a hand-designed block based CS recovery algorithm. Experimental results demonstrate that the proposed method outperforms the state-of-the-art CS methods by a large margin in terms of objective metrics and subjective visual image quality. Our source codes are available at https://github.com/siwangzhou/DeepBCS.