Compressive Sensing Algorithm Research Articles

Block compressed sensing image reconstruction via deep learning with smoothed projected Landweber

Compressed sensing (CS) is a signal processing framework for effectively reconstructing signal from a small number of measurements obtained by linear projections of the signal. It is an ongoing challenge for the real-time image reconstruction of the computational imaging, including single pixel imaging based on CS. We built a block-based CS (BCS) image reconstruction framework via a deep learning network with smoothed projected Landweber (SPL). A fully connected network performs both BCS linear sensing and non-linear reconstruction stages, and SPL removes the blocking artifacts due to incorporate Wiener filtering into projected Landweber (PL) method at each iteration. The sensing matrix and nonlinear prediction operator are jointly optimized, and the smoothing filtering is coalesced into the PL framework for eliminating high-frequency oscillatory blocking artifact. Experimental results reveal that the optimized scheme outperforms the approach only based on deep neural network. The reconstruction quality can be improved while being only slightly slower, especially the gain of structural similarity is significantly better than peak signal-to-noise ratio, and the reconstruction image texture details are vivid and natural. At 10% sensing rate, the structural similarity maximum (minimum) gain reaches 0.098 (0.021). The proposed approach is not only far superior to other state-of-the-art CS algorithms in terms of reconstruction time and quality but also comparable with up-to-date deep learning methods.

Compressive sensing of wind speed data of large-scale spatial structures with dedicated dictionary using time-shift strategy

The real-time wind monitoring is widely used to evaluate the wind effect on the large-scale spatial structures. Wireless sensor network (WSN) is usually the first choice for the large-scale spatial structures to collect wind monitoring data because of its super-large size. Compressive sensing (CS) has great potential in solving the energy problem of WSN and reduces the difficulty in transmission of massive data based on sparsity. However, wind signals are often not naturally sparse on the traditional bases (e.g., Fourier basis). This paper proposes a new method of constructing a dedicated dictionary for wind speed signals using the time-shift strategy. With this proposed dictionary, the signals can be compressed by random sampling and recovered by ℓ1-norm sparse regularization. The performance of the improved CS methodology is evaluated using two large-scale spatial structures. The results show that the proposed CS methodology has better performance than the traditional CS algorithm with the Fourier basis and the linear interpolation method. Furthermore, the influences of the relevant critical parameters (regularization parameter, lag, sliding window size, and compression ratio) of the improved CS methodology are comprehensively explored.

High Frequency Edge Information-based Sampling Algorithm for Multi-scale Block Compressive Sensing

The same sampling rate is applied to all subblocks of the same layer, which results in the deviation of the information contained in the sampling observation in the multi-scale block compressive sensing algorithm from the real information of the original image, thus affecting the accuracy of image reconstruction. For this reason, the multi-scale block compressive sensing adaptive sampling method (HEM) using HF edge information is proposed. In this method, the edge information is extracted by using the high frequency coefficients of wavelet transform, and then the edge information of the subblock of wavelet decomposition graph is calculated, and then converted into the adaptive sampling rate of each subblock. The influence of different decomposition layers and block sizes on HEM method is discussed through testing in 6 standard images. The experimental results show that the proposed algorithm can improve the PSNR of the reconstructed image at the same sampling rate on standard test images and cable trench inspection images. Among them, Stanwick image(S=0.1 and S=0.2), Russland image(S=0.3) and Stomach CT image(S=0.4) are partial exceptions.

Impact of optimal scaling coefficients in bi-orthogonal wavelet filters on compressed sensing

PurposeIn today’s digital world, real-time health monitoring is becoming a most important challenge in the field of medical research. Body signals such as electrocardiogram (ECG), electromyogram and electroencephalogram (EEG) are produced in human body. This continuous monitoring generates huge count of data and thus an efficient method is required to shrink the size of the obtained large data. Compressed sensing (CS) is one of the techniques used to compress the data size. This technique is most used in certain applications, where the size of data is huge or the data acquisition process is too expensive to gather data from vast count of samples at Nyquist rate. This paper aims to propose Lion Mutated Crow search Algorithm (LM-CSA), to improve the performance of the LMCSA model.Design/methodology/approachA new CS algorithm is exploited in this paper, where the compression process undergoes three stages: designing of stable measurement matrix, signal compression and signal reconstruction. Here, the compression process falls under certain working principle, and is as follows: signal transformation, computation of Θ and normalization. As the main contribution, the theta value evaluation is proceeded by a new “Enhanced bi-orthogonal wavelet filter.” The enhancement is given under the scaling coefficients, where they are optimally tuned for processing the compression. However, the way of tuning seems to be the great crisis, and hence this work seeks the strategy of meta-heuristic algorithms. Moreover, a new hybrid algorithm is introduced that solves the above mentioned optimization inconsistency. The proposed algorithm is named as “Lion Mutated Crow search Algorithm (LM-CSA),” which is the hybridization of crow search algorithm (CSA) and lion algorithm (LA) to enhance the performance of the LM-CSA model.FindingsFinally, the proposed LM-CSA model is compared over the traditional models in terms of certain error measures such as mean error percentage (MEP), symmetric mean absolute percentage error (SMAPE), mean absolute scaled error, mean absolute error (MAE), root mean square error, L1-norm and L2-normand infinity-norm. For ECG analysis, under bior 3.1, LM-CSA is 56.6, 62.5 and 81.5% better than bi-orthogonal wavelet in terms of MEP, SMAPE and MAE, respectively. Under bior 3.7 for ECG analysis, LM-CSA is 0.15% better than genetic algorithm (GA), 0.10% superior to particle search optimization (PSO), 0.22% superior to firefly (FF), 0.22% superior to CSA and 0.14% superior to LA, respectively, in terms of L1-norm. Further, for EEG analysis, LM-CSA is 86.9 and 91.2% better than the traditional bi-orthogonal wavelet under bior 3.1. Under bior 3.3, LM-CSA is 91.7 and 73.12% better than the bi-orthogonal wavelet in terms of MAE and MEP, respectively. Under bior 3.5 for EEG, L1-norm of LM-CSA is 0.64% superior to GA, 0.43% superior to PSO, 0.62% superior to FF, 0.84% superior to CSA and 0.60% better than LA, respectively.Originality/valueThis paper presents a novel CS framework using LM-CSA algorithm for EEG and ECG signal compression. To the best of the authors’ knowledge, this is the first work to use LM-CSA with enhanced bi-orthogonal wavelet filter for enhancing the CS capability as well reducing the errors.

Generalized Sparse Polarization Array for DOA Estimation Using Compressive Measurements

The compressive array method, where a compression matrix is designed to reduce the dimension of the received signal vector, is an effective solution to obtain high estimation performance with low system complexity. While sparse arrays are often used to obtain higher degrees of freedom (DOFs), in this paper, an orthogonal dipole sparse array structure exploiting compressive measurements is proposed to estimate the direction of arrival (DOA) and polarization signal parameters jointly. Based on the proposed structure, we also propose an estimation algorithm using the compressed sensing (CS) method, where the DOAs are accurately estimated by the CS algorithm and the polarization parameters are obtained via the least‐square method exploiting the previously estimated DOAs. Furthermore, the performance of the estimation of DOA and polarization parameters is explicitly discussed through the Cramér‐Rao bound (CRB). The CRB expression for elevation angle and auxiliary polarization angle is derived to reveal the limit of estimation performance mathematically. The difference between the results given in this paper and the CRB results of other polarized reception structures is mainly due to the use of the compression matrix. Simulation results verify that, compared with the uncompressed structure, the proposed structure can achieve higher estimated performance with a given number of channels.

Efficient 3D Image Reconstruction of Airborne TomoSAR Based on Back Projection and Improved Adaptive ISTA

Airborne SAR tomography (TomoSAR) 3D image reconstruction can be realized with combination of 2D imaging algorithms and compressed sensing (CS) algorithms. However, most typical CS algorithms cannot achieve a balance between algorithm efficiency and 3D reconstruction accuracy. Due to difficulties in flight path control of airborne SAR, it is hard to realize registration of SAR images with frequency-domain imaging algorithms because of time-varying baseline. To address these problems, an efficient 3D image reconstruction method for airborne TomoSAR based on back projection (BP) algorithm and improved adaptive iterative shrinkage-thresholding algorithm (IA-ISTA) is proposed. First, 2D images are achieved with BP algorithm on the ground plane. After registration of SAR images, 3D image reconstruction results in the elevation direction are realized with IA-ISTA. Selection criterion of IA-ISTA parameters are given in this paper. At last, final 3D image reconstruction results are achieved after geometrical transformation based on geometric relationship. Both simulated data and measured data of a P-band airborne TomoSAR system are used. 3D image reconstruction results show that the proposed method outperforms traditional methods regarding efficiency and accuracy, which proves the validity and practicality of the proposed method.

Compressed Sensing-Based Simultaneous Recovery of Magnitude and Phase MR Images via Dual Trigonometric Sparsity

Complex-valued Magnetic Resonance Imaging (MRI) is widely used in clinical diagnosis. The magnitude images are mainly used for structure visualization, and the phase images reveal tissue properties, such as magnetic susceptibility and fluid flow information. While MRI is slow, compressed sensing (CS) can be used to reconstruct the accelerated acquisitions. Current CS-based MRI reconstruction algorithms mostly focus on magnitude image recovery, with less attention to the recovery of phase images. In this paper, we propose a novel CS algorithm to simultaneously recover the magnitude and phase MR images based on the sparsity of the trigonometric function. The CS method requires a sparse representation of the original images, and it is observed the trigonometric functions of phase images in the Wavelet domain promote sparsity. Therefore, rather than transforming the phase images directly into the Wavelet domain, we calculate the sine and cosine of the phase images whose Wavelet transforms are set as the L1-norm regularization term. The combination of the dual trigonometric functions captures a unique, faithful four-quadrant phase information, which also improves the reconstructed magnitude images through an alternating optimization procedure. Reconstructions of simulated images and in vivo images are studied, and both show the superiority of the proposed method over compared phase recovery algorithms.

A Photoacoustic Imaging Algorithm Based on Regularized Smoothed L0 Norm Minimization.

The recently emerging technique of sparse reconstruction has received much attention in the field of photoacoustic imaging (PAI). Compressed sensing (CS) has large potential in efficiently reconstructing high-quality PAI images with sparse sampling signal. In this article, we propose a CS-based error-tolerant regularized smooth L0 (ReSL0) algorithm for PAI image reconstruction, which has the same computational advantages as the SL0 algorithm while having a higher degree of immunity to inaccuracy caused by noise. In order to evaluate the performance of the ReSL0 algorithm, we reconstruct the simulated dataset obtained from three phantoms. In addition, a real experimental dataset from agar phantom is also used to verify the effectiveness of the ReSL0 algorithm. Compared to three L0 norm, L1 norm, and TV norm-based CS algorithms for signal recovery and image reconstruction, experiments demonstrated that the ReSL0 algorithm provides a good balance between the quality and efficiency of reconstructions. Furthermore, the PSNR of the reconstructed image calculated by the introduced method was better than the other three methods. In particular, it can notably improve reconstruction quality in the case of noisy measurement.

Low-Complexity Implementation of Channel Estimation for ESPAR-OFDM Receiver

Electronically steerable parasitic array radiator (ESPAR) antenna is a novel low-cost technique to gain comparable diversity order to that of using multiple antennas while maintaining one radio frequency (RF) front-end, low power consumption, and simple wiring at the mobile receiver. It has huge potential to realize high energy efficiency for multiple and massive antennas systems. The main drawback of the ESPAR based OFDM system is that the channel estimation (CE) usually should be realized in time-domain with a huge computational complexity (CC) because the received signal to each parasitic element is overlapped each other both in frequency and time domain. This article will propose three ways to reduce the complexity of CE for the ESPAR-OFDM system. The parallel multi-column compressive sensing (CS) algorithm was first introduced to detect all locations of channel impulse response simultaneously using one small segment of sensing matrix. Furthermore, by exploiting the symmetrical properties of Digital Fourier transform (DFT), the size of matrix to decrease the CC of matrix operation. Finally, by selecting a small set of row vectors of sensing matrix at the receiver side, the CC involved in CS algorithm can be reduced. From the analysis and simulated results, the proposed method can obtain more than 90% CC reduction for CE of ESPAR-OFDM receiver can be confirmed.

Joint communication and radar sensing in 5G mobile network by compressive sensing

Radio sensing can be integrated with communication in what the authors call future perceptive mobile networks. Due to the complicated signal structure, it is challenging to estimate sensing parameters such as delay, angle of arrival, and Doppler when joint communication and radar/radio sensing is applied in perceptive mobile networks. Radio sensing with signals compatible with a fifth-generation (5G) new radio standard using one-dimension (1D) to 3D compressive sensing (CS) techniques under 5G channel conditions is studied. In the case of 1D–3D CS techniques, they formulate the parameter estimation as a sparse signal recovery problem. These algorithms demonstrate respective advantages, but also show shortcomings in dealing with clustered channels. To effectively exploit the cluster structure in multipath channels, they also propose a 2D cluster Kronecker CS algorithm for significantly improved sensing parameter estimation via introducing a prior probability distribution. Simulation results are provided and they focus the respective advantages and disadvantages of these techniques that validate the effectiveness of the proposed algorithms.

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.

Compressed sensing and the use of phased array coils in 23Na MRI: a comparison of a SENSE-based and an individually combined multi-channel reconstruction

PurposeTo implement and to evaluate a compressed sensing (CS) reconstruction algorithm based on the sensitivity encoding (SENSE) combination scheme (CS-SENSE), used to reconstruct sodium magnetic resonance imaging (23Na MRI) multi-channel breast data sets. MethodsIn a simulation study, the CS-SENSE algorithm was tested and optimized by evaluating the structural similarity (SSIM) and the normalized root-mean-square error (NRMSE) for different regularizations and different undersampling factors (USF=1.8/3.6/7.2/14.4). Subsequently, the algorithm was applied to data from in vivo measurements of the healthy female breast (n=3) acquired at 7T. Moreover, the proposed CS-SENSE algorithm was compared to a previously published CS algorithm (CS-IND). ResultsThe CS-SENSE reconstruction leads to an increased image quality for all undersampling factors and employed regularizations. Especially if a simple 2nd order total variation is chosen as sparsity transformation, the CS-SENSE reconstruction increases the image quality of highly undersampled data sets (CS-SENSE: SSIMUSF=7.2=0.234, NRMSEUSF=7.2=0.491 vs. CS-IND: SSIMUSF=7.2=0.201, NRMSEUSF=7.2=0.506). ConclusionThe CS-SENSE reconstruction supersedes the need of CS weighting factors for each channel as well as a method to combine single channel data. The CS-SENSE algorithm can be used to reconstruct undersampled data sets with increased image quality. This can be exploited to reduce total acquisition times in 23Na MRI.

Contention-based nonorthogonal massive access with massive MIMO

The sporadic communication character of massive machine-type communication systems provides natural advantages to utilize the principle of compressive sensing (CS). However, due to the high computational complexity of CS algorithms, CS-based contention-free access schemes have limited scalability and high computational complexity for massive access with user-specific pilots. To address these problems, in this paper, we propose a new contention-based scheme for CS-based massive access, which can support the sporadic access of massive devices (more than one million devices) with limited resources. Furthermore, an advanced receiver algorithm is designed to solve the optimal solutions for the proposed scheme, which utilizes various prior information to enhance the performance. In specific, the joint sparsity between the channel and data is used to improve the accuracy of pilot detection, and the information of modulation and cyclic redundancy check is exploited for channel correction to improve the performance of data recovery. The simulation results show that the proposed scheme can achieve improved active user detection performance and data recovery accuracy than existing methods.

Efficient Optical MIMO–OFDM Channel Estimation Based on Correntropy Compressive Sensing

The compressive sensing (CS) technique is widely used in the field of radio-frequency channel estimation. However, in optical wireless channel (OWC) estimation, CS needed to be adapted to cope with the nonlinear distortion resultant from the electrical-to-optical and optical-to-electrical conversion process of the OWC. Therefore, a robust CS channel estimation technique is proposed for the optical MIMO–OFDM system. The proposed CS channel estimation technique is based on higher-order statistics (HOS). In which, the correntropy is exploited as a HOS similarity measurement instead of the second-order statistics euclidean distance (ED) used with the conventional CS to handle the OWC nonlinear distortion. Herein, the ED is the most popular iterative CS algorithms such as orthogonal matching pursuits, sparsity adaptive matching pursuit, and self-aware step size sparsity adaptive matching pursuit is efficiently replaced by the HOS correntropy based CS to show the effectiveness of the proposed algorithm. Moreover, the most recent visible light communication system GLIM-OFDM is considered here to test the proposed technique. However, the pre-estimated channel state information (CSI) obtained from the previous OFDM frame is exploited as initial information in estimating the CSI of the current OFDM frame, which improves overall system performance. A comparison with the conventional CS reconstruction algorithms is conducted via extensive simulation analysis. The simulation results show the superiority of the bit error rate of the proposed correntropy based CS channel estimation scheme compared to the conventional CS-based channel estimation algorithms.

Deep Learning-Based Denoise Network for CSI Feedback in FDD Massive MIMO Systems

Channel state information (CSI) feedback is critical for frequency division duplex (FDD) massive multi-input multi-output (MIMO) systems. Most conventional algorithms are based on compressive sensing (CS) and are highly dependent on the level of channel sparsity. To address the issue, a recent approach adopts deep learning (DL) to compress CSI into a codeword with low dimensionality, which has shown much better performance than the CS algorithms when feedback link is perfect. In practical scenario, however, there exists various interference and non-linear effect. In this article, we design a DL-based denoise network, called DNNet, to improve the performance of channel feedback. Numerical results show that the DL-based feedback algorithm with the proposed DNNet has superior performance over the existing algorithms, especially at low signal-to-noise ratio (SNR).

Fast two‐dimensional sparse signal gridless recovery algorithm for MIMO array SAR 3D imaging

Multiple-input multiple-output (MIMO) array synthetic aperture radar (SAR) can be used to directly obtain the three-dimensional (3D) imagery of the illuminated scene with a single track. Due to the length limitations of synthetic aperture and antenna array, the super-resolution algorithms within the framework of 2D compressive sensing (CS) have been conceived to reconstruct the azimuth-cross-track plane image because of its spatial sparsity. Since the desired scatterers are presupposed to be distributed over a series of fixed grid points, the location accuracy of the existing 2D CS algorithms is relatively low. To overcome this problem, a fast 2D gridless recovery (GLR) algorithm for the 2D imaging signal model established in the real domain is proposed in this study. First, two different forms of 2D real-valued signal models with uniform or random sampling on the azimuth-cross-track plane are reconstructed by means of unitary transformation. Further, the real-domain based 2D sparse signal gridless reconstruction approach is derived. Finally, extensive simulation results validate that the proposed 2D real-valued GLR approach can approximately improve the computational efficiency by a factor of ten in terms of CPU time when compared with that of the 2D GLR algorithm in the complex domain.

Recovering compressed images for automatic crack segmentation using generative models

In a structural health monitoring (SHM) system that uses digital cameras to monitor cracks of structural surfaces, techniques for reliable and effective data compression are essential to ensure a stable and energy-efficient crack images transmission in wireless devices, e.g., drones and robots with high definition cameras installed. Compressive sensing (CS) is a signal processing technique that allows accurate recovery of a signal from a sampling rate much smaller than the limitation of the Nyquist sampling theorem. Different from the popular approach of simultaneously training encoder and decoder using neural network models, the CS theory ensures a high probability of accurate signal reconstruction based on random measurements that is shorter than the length of the original signal under a sparsity constraint. Such method is particularly useful when measurements are expensive, such as wireless sensing of civil structures, because its hardware implementation allows down sampling of signals during the sensing process. Hence, CS methods can achieve significant energy saving for the sensing devices. However, the strong assumption of the signals being highly sparse in an invertible space is relatively hard to guarantee for many real images, such as image of cracks. In this paper, we present a new approach of CS that replaces the sparsity regularization with a generative model that is able to effectively capture a low dimension representation of targeted images. We develop a recovery framework for automatic crack segmentation of compressed crack images based on this new CS method. We demonstrate the remarkable performance of our method that takes advantage of the strong capability of generative models to capture the necessary features required in the crack segmentation task even the backgrounds of the generated images are not well reconstructed. The superior performance of our recovery framework is illustrated by comparisons to three existing CS algorithms. Furthermore, we show that our framework is potentially extensible to other common problems in automatic crack segmentation, such as defect recovery from motion blurring and occlusion.

The relevance vector machine for seismic Bayesian compressive sensing

Missing traces in seismic surveys create gaps in the data and cause problems in later stages of the seismic processing workflow through aliasing or incoherent noise. Compressive sensing (CS) is a framework that encompasses data reconstruction algorithms and acquisition processes. However, CS algorithms are mainly ad hoc by focusing on data reconstruction without any uncertainty quantification or feature learning. To avoid ad hoc algorithms, a probabilistic data-driven model is used, the relevance vector machine (RVM), to reconstruct seismic data and simultaneously quantify uncertainty. Modeling of sparsity is achieved using dictionaries of basis functions, and the model remains flexible by adding or removing them iteratively. Random irregular sampling with time-slice processing is used to reconstruct data without aliasing. Experiments on synthetic and field data sets illustrate its effectiveness with state-of-the-art reconstruction accuracy. In addition, a hybrid approach is used in which the domain of operation is smaller while, simultaneously, learned dictionaries of basis functions from seismic data are used. Furthermore, the uncertainty in predictions is quantified using the predictive variance of the RVM, obtaining high uncertainty when the reconstruction accuracy is low and vice versa. This could be used for the evaluation of source/receiver configurations guiding seismic survey design.

Distribution agnostic Bayesian matching pursuit based on the exponential embedded family

Compressed sensing (CS) is an emerging field that allows to recover high-dimensional sparse signal from a few compressed measurements. Classical CS algorithms using the Bayesian framework generally impose a sparseness-promoting prior on the signal, which may not characterize the real signals with diversity. Moreover, estimating the parameters involved in the prior is challenging especially for non-i.i.d. signals. In this paper, we propose an efficient prior-agnostic Bayesian matching pursuit for sparse signal recovery, which avoids the risk of imposing mismatched prior on the signals and enjoys lower complexity than Bayesian approaches due to the elimination of prior parameter estimation. Specifically, we utilize the noise model and the reduced exponential embedded family (EEF) to obtain an approximate likelihood of interest, and then find the most dominant supports with maximum approximate likelihoods in a greedy manner to give an approximate minimum mean squared error (MMSE) estimate for the sparse signal. Experiment results demonstrate that our method achieves lower normalized mean squared error (NMSE) while higher efficiency compared to the state-of-the-art methods.

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.