Sparse Recovery Algorithm Research Articles

Heavy-ball-based hard thresholding algorithms for sparse signal recovery

The hard thresholding technique plays a vital role in the development of algorithms for sparse signal recovery. By merging this technique and heavy-ball acceleration method which is a multi-step extension of the traditional gradient descent method, we propose the so-called heavy-ball-based hard thresholding (HBHT) and heavy-ball-based hard thresholding pursuit (HBHTP) algorithms for signal recovery. It turns out that the HBHT and HBHTP can successfully recover a k-sparse signal if the restricted isometry constant of the measurement matrix satisfies δ3k<0.618 and δ3k<0.577, respectively. The guaranteed success of HBHT and HBHTP is also shown under the conditions δ2k<0.356 and δ2k<0.377, respectively. Moreover, the finite convergence of HBHTP and stability of the two algorithms are also established in this paper. Simulations on random problem instances are performed to compare the performance of the proposed algorithms and several existing ones. Empirical results indicate that the HBHTP performs very comparably to a few existing algorithms and it takes less average time to achieve the signal recovery than these existing methods.

Parallel matching pursuit algorithm and analysis

For the existing compressed sensing greedy reconstruction algorithm, it is easy to fall into local optimum and overfitting problems. In this paper, we propose a new sparse recovery algorithm, called Parallel Matching pursuit (PMP), which searches the signal support set in both depth and breadth dimensions. PMP simultaneously examines multiple estimates of candidate support set in each iteration, and finally chooses the estimate that minimizes the reconstruction residual. Based on the restricted isometry property (RIP), sufficient conditions for PMP to reconstruct the signal are given to ensure that we can accurately recover any K-sparse signal from the measured value. Moreover, the recovery guarantee of the PMP algorithm is also provided for the case of noisy measurements. The performance of the PMP algorithm is evaluated by the signal reconstruction ability. Finally, numerical experiments verify the effectiveness of the algorithm.

Performance analysis of compressive sensing and reconstruction by LASSO and OMP for audio signal processing applications

Audio signal processing is used in acoustic IoT sensor nodes which have limitations in data storage, computation speed, hardware size and power. In most audio signal processing systems, the recovered data constitutes far less fraction of the sampled data providing scope for compressive sensing (CS) as an efficient way for sampling and signal recovery. Compressive sensing is a signal processing technique in which a sparse approximated signal is reconstructed at the receiving node by a signal recovery algorithm, using fewer samples compared to traditional sampling methods. It has two main stages: sparse approximation to convert the signal into a sparse domain and reconstruction through sparse signal recovery algorithms. Recovery algorithms involve complex matrix multiplication and linear equations in sampling and reconstruction, increasing the computational complexity and leading to highly resourceful hardware implementations. This work reconstructs the sparse audio signal using LASSO and orthogonal matching pursuit (OMP) algorithm. OMP is an iterative greedy algorithm involving least square method that takes a compressed signal as input and recovers it from the sparse approximation, while LASSO is L1 norm based with a controlled L2 penalty. The paper reviews the reconstruction and study of sparsity and error obtained for reconstructing an audio signal by OMP and LASSO.

Target parameter estimation for OTFS radar using sparse signal processing

In this paper, we consider a monostatic radar receiver for a joint communication and radar (JCR) system that transmits orthogonal time frequency space (OTFS) frames for target detection and parameter estimation. The circular prolate pulse shape (CPPS) is employed over the OTFS signal as it has lower out-of-band (OoB) power radiation in comparison with the rectangular pulse shaped (RPS) OTFS. The PAPR of CPPS OTFS signal shows lowest value for larger frame duration and hence the signal can be considered to be a good candidate for JCR system. In the Delay-Doppler (DD) domain, the radar channel is sparse and therefore, we model the target detection problem as a sparse recovery problem to generate target profiles with higher peak-to-sidelobe ratio (PSLR). The target detection is carried out in the DD domain, the time–frequency (TF) domain, and in the time domain (TD). Sparse signal recovery algorithms like the orthogonal matching pursuit (OMP) algorithm, the subspace pursuit (SP) algorithm, and the sparse Bayesian learning (SBL) based algorithm are used in target parameter estimation. The performance of these algorithms are compared in terms of their computational complexity, the root mean squared error (RMSE) in the estimates of range and velocity and PSLR value in the target profiles. Simulation results validate that the proposed CPPS OTFS based radar system could detect the targets accurately in all the three domains and produce target profiles with almost zero side lobes.

On sparse recovery algorithms in unions of orthonormal bases

We are concerned with the problem of recovering sparse vectors exactly by two commonly used methods, orthogonal matching pursuit (OMP) and basis pursuit (BP). Suppose that overcomplete dictionaries are unions of several orthonormal bases. Gribonval and Nielsen have provided a sufficient mutual coherence condition for BP to recover every sparse vector exactly. Then Tropp proved that it is a sharp sufficient condition for OMP by existence proofs. We establish here the sharpness of Gribonval and Nielsen’s sufficient condition for both OMP and BP by constructing several families of counterexamples. Our main tools are Hadamard matrices and mutually unbiased bases from quantum information theory.

Deep Learning-Based Activity Detection for Grant-Free Random Access

The cellular Internet of Things wireless network is a promising solution to provide massive connectivity for machine-type devices. However, designing grant-free random access (GF-RA) protocols to manage such connections is challenging, since they must operate in interference-aware scenarios with sporadic device activation patterns and a shortage of mutually orthogonal resources. Supervised machine learning models have provided efficient solutions for activity detection, noncoherent data detection, and nonorthogonal preamble design in scenarios with massive connectivity. In this article, we develop two deep learning (DL) sparse support recovery algorithms to detect active devices in massive machine-type communication random access. The DL algorithms, developed to deploy GF-RA protocols, are based on the deep multilayer perceptron and the convolutional neural network models. Unlike previous works, we investigate the impact of the type of sequences for preamble design on the activity detection accuracy. Our results reveal that preambles based on the Zadoff–Chu sequences, which present good correlation properties, achieve better activity detection accuracy with the proposed algorithms than random sequences. Besides, we demonstrate that our DL algorithms achieve activity detection accuracy comparable to state-of-the-art techniques with extremely low computational complexity.

Tree-Search-Based Optimal and Suboptimal Low Complexity Detectors for Differential Space Shift Keying MIMO System

This article proposes two low complexity decoders for non coherent differential space shift keying (DSSK) multiple input multiple output (MIMO) system by representing the detection problem as a hierarchical tree structure. Such presentation enables yielding the optimal maximum likelihood (ML) performance but with a massive reduction in computational complexity. Attained reduction is accomplished through 1) utilizing the error-repetitive property of DSSK detection to reduce the number of computed error terms and 2) developing two efficient searching strategies that avoid searching the entire alphabet as in ML detectors. These searching strategies enable a trade–off between performance and complexity. Unlike existing sparse recovery (SR) decoders, which require a projection phase to ensure the closure property (i.e., only single transmit antenna is active at each particular time instant and the multiplication of a constellation matrix with another one will produce a matrix from within the set), the new algorithms, inherently, maintain the closure property of DSSK system without additional procedures. Reported results reveal that optimal ML performance is obtained with a huge reduction in complexity by proper adjustment of parameters. It is also shown that the proposed algorithm performs better than state of the art SR algorithms, and the feasibility of massive MIMO configurations with low complexity is demonstrated.

Optimizing Sensing Matrices for Spherical Near-Field Antenna Measurements

In this article, we address the problem of reducing the number of required samples for spherical near-field (SNF) antenna measurements by using compressed sensing (CS). A condition to ensure the numerical performance of sparse recovery algorithms is the design of a sensing matrix with low mutual coherence. Without fixing any part of the sampling pattern, we directly find sampling points that minimize the mutual coherence of the respective sensing matrix. Numerical experiments show that the proposed sampling scheme yields a higher recovery success in terms of phase transition diagram when compared to other known sampling patterns, such as the spiral and Hammersley sampling schemes. Furthermore, we also demonstrate that the application of CS with an optimized sensing matrix requires fewer samples than classical approaches to reconstruct the spherical mode coefficients (SMCs) and far-field pattern.

Sparse recovery algorithm via adaptive grids for linear array SAR 3D sparse imaging

ABSTRACT Compressed sensing (CS) algorithms mostly achieve linear array synthetic aperture radar (LASAR) 3D sparse imaging under the On-Grid strategy, they suffer from the mismatch measurement matrix and decreased imaging quality due to the position-errors among targets and preset scattering units. Aimed at this problem, based on the Off-Grid strategy, a sparse recovery algorithm via adaptive grids (SRAG) is proposed in this paper. First, the proposed algorithm extracts the target scattering units in the imaging scene under the On-Grid strategy. Second, the target scattering units with position-errors are extracted under the non-zero adjacent scattering coefficient criterion, and they are defined as the unfocused scattering units. Third, according to whether the unfocused scattering units’ distance is smaller than the scattering unit spacing, their search-areas of targets’ real positions are set, respectively, and differently. Finally, based on the minimum scattering coefficient residual criterion, we adaptively compensate the unfocused scattering units’ position-errors and re-estimate their scattering coefficients. Both simulation and experimental results indicate that the SRAG algorithm decreases the position-errors effectively, it improves the imaging quality, estimation accuracy of targets’ positions, and scattering coefficients than traditional On-Grid CS algorithms.

A High-Resolution Imaging Method for ISAR Based on Sparse Reconstruction

For the problem of first-order and second-order range migration in ISAR imaging under the condition of wide angle and wide bandwidth, a method for sparse azimuth data is proposed to obtain high-resolution ISAR images. After stretch processing, envelope alignment and residual video phase removal, the sparse recovery algorithm that sparse base is constructed by the Keystone transform is used to achieve range migration correction and the missing range profile reconstruction, and then the second-order phase estimation method based on fractional Fourier transform is used to estimate and compensate the second-order rotational phase. Simulation results show the method can effectively improve the imaging quality.

Estimation of Time-Varying Channels in Virtual Angular Domain for Massive MIMO Systems

This paper is concerned with the problem of channel estimation in virtual angular domain in massive MIMO orthogonal frequency division multiplexing (OFDM) systems, in the presence of time varying channels. The proposed channel estimator is based on dichotomous coordinate decent joint sparse recovery (DCD-JSR) algorithm, which was well suited for massive MIMO systems with channels static over several OFDM symbols, but it is not accurate for time-varying channels. The estimator proposed in this paper exploits the basis expansion model (BEM) for approximation of the time-variation of the channel and the sparsity of the channel in the virtual angular domain with a common support over OFDM subcarriers and OFDM symbols for joint estimation of the BEM expansion coefficients. It is shown that, when using the Legendre polynomials as the BEM and depending on the normalized Doppler frequency, only a small number of expansion coefficients is required to provide accurate channel estimation.

Improved Sufficient Conditions Based on RIC of Order 2s for IHT and HTP Algorithms

Reconstructing an s-sparse signal x from an un- derdetermined noisy linear model arises in many applications. The iterative hard thresholding (IHT) and hard thresholding pursuit (HTP) algorithms are two popular sparse signal recovery algorithms. Since their recovery performances can be theoreti- cally characterized by their sufficient conditions of stable sparse signal recovery, it is essential to establish less restrictive sufficient conditions. This work develops δ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2s</sub> -based sufficient conditions for stable recovery with IHT and HTP. The two new sufficient conditions are significantly less restrictive than the state-of-the- art ones for IHT and HTP.

Infrared Small Target Detection With Patch Tensor Collaborative Sparse and Total Variation Constraint

Sparse and low-rank modeling has shown a powerful describing abilities to express small target, however, low-rank model exists the problem of insufficient rank approximation deviation ability and excessive shrinkage, which will lead to inaccurate background estimation. In this letter, a new non-convex approximation function using Gaussian model is built toward deeply excavating low-rank information of background as much as possible. In the sparse collaborative representation, the local prior confidence (LPC) is integrated into the target structure tensor to maximum to distinguish target region and background edge more accurately. In the process of background restoration, total variation constraint (TVC) is employed apropos of describing gray variation of small target in complex background more precisely and improving accuracy of background restoration to further perfectly recover small targets. The low-rank and sparse recovery algorithm engages alternating direction multiplier method (ADMM) for iterative calculation and solution. Compared with advanced optimal algorithms, a great number of experimental results show that the proposed model improves the adaptability and robustness of the detection algorithm to variety of complex scenes, and has lasting vitality and high application value.

A Sparse Recovery Algorithm Based on Arithmetic Optimization

At present, the sparse recovery problem is mainly solved by convx optimization algorithm and greedy tracking method. However, the former has defects in recovery efficiency and the latter in recovery ability, and neither of them can obtain effective recovery under large sparsity or small observation degree. In this paper, we propose a new sparse recovery algorithm based on arithmetic optimization algorithm and combine the ideas of greedy tracking method. The proposed algorithm uses arithmetic optimization algorithm to solve the sparse coefficient of the signal in the transform domain, so as to reconstruct the original signal. At the same time, the greedy tracking technique is combined to design the initial position of the operator before solving, so that it can be searched better. Experiments show that compared with other methods, the proposed algorithm can not only obtain more effective recovery, but also run faster under general conditions of observation number. At the same time, It can also recover the signal better in the presence of noise.

Hyperspectral detection of fresh corn peeling damage using germinating sparse classification method.

Peeling damage reduces the quality of fresh corn ear and affects the purchasing decisions of consumers. Hyperspectral imaging technique has great potential to be used for detection of peeling-damaged fresh corn. However, conventional non-machine-learning methods are limited by unsatisfactory detection accuracy, and machine-learning methods rely heavily on training samples. To address this problem, the germinating sparse classification (GSC) method is proposed to detect the peeling-damaged fresh corn. The germinating strategy is developed to refine training samples, and to dynamically adjust the number of atoms to improve the performance of dictionary, furthermore, the threshold sparse recovery algorithm is proposed to realize pixel level classification. The results demonstrated that the GSC method had the best classification effect with the overall classification accuracy of the training set was 98.33%, and that of the test set was 95.00%. The GSC method also had the highest average pixel prediction accuracy of 84.51% for the entire HSI regions and 91.94% for the damaged regions. This work represents a new method for mechanical damage detection of fresh corn using hyperspectral image (HSI).

Model-Based Deep Learning for Joint Activity Detection and Channel Estimation in Massive and Sporadic Connectivity

We present two model-based neural network architectures purposed for sporadic user detection and channel estimation in massive machine-type communications. In the scenario under consideration, a base station assigns the users a set of pilot sequences that is linearly dependent, but because user activity is sporadic the detection/estimation problem is amenable to sparse recovery algorithms. Further, we consider a millimeter-wave wireless channel, so that the channel vectors are sparse in a known dictionary. We apply the deep unfolding framework to design custom neural network layers by unrolling two iterative optimization algorithms: (1) linearized alternating direction method of multipliers, which we apply to a constrained convex problem, and (2) vector approximate message passing featuring a novel denoiser based on the iterative shrinkage thresholding algorithm. The networks thus inherit domain knowledge as encapsulated by the signal model, and suitable operations as informed by the algorithms—in the same spirit as convolutional networks that exploit structure inherent in images and audio, except grounded in optimization and statistics. The networks, trained on synthetic data generated from the block-fading millimeter-wave multiple access channel model, offer improved complexity and accuracy relative to their iterative counterparts, and are potentially a boon to cell-free MIMO systems.

A Novel Detector based on Compressive Sensing for Uplink Massive MIMO Systems

Massive multiple-input multiple-output is a promising technology in future communication networks where a large number of antennas are used. It provides huge advantages to the future communication systems in data rate, the quality of services, energy efficiency, and spectral efficiency. Linear detection algorithms can achieve a near-optimal performance in large-scale MIMO systems, due to the asymptotic orthogonal channel property. But, the performance of linear MIMO detectors degrades when the number of transmit antennas is close to the number of receive antennas (loaded scenario). Therefore, this paper proposes a series of detectors for large MIMO systems, which is capable of achieving promising performance in loaded scenarios. The main idea is to improve the performance of the detector by finding the hidden sparsity in the residual error of the received signal. At the first step, the conventional MIMO model is converted into the sparse model via the symbol error vector obtained from a linear detector. With the aid of the compressive sensing methods, the incorrectly detected symbols are recovered and performance improvement in the detector output is obtained. Different sparse recovery algorithms have been considered to reconstruct the sparse error signal. This study reveals that error recovery by imposing sparse constraint would decrease the bit error rate of the MIMO detector. Simulation results show that the iteratively reweighted least squares method achieves the best performance among other sparse recovery methods.

Sparsity-Based Two-Dimensional DOA Estimation for Co-Prime Planar Array via Enhanced Matrix Completion

In this paper, the two-dimensional (2-D) direction-of-arrival (DOA) estimation problem is explored for the sum-difference co-array (SDCA) generated by the virtual aperture expansion of co-prime planar arrays (CPPA). Since the SDCA has holes, this usually causes the maximum virtual aperture of CPPA to be unavailable. To address this issue, we propose a complex-valued, sparse matrix recovery-based 2-D DOA estimation algorithm for CPPA via enhanced matrix completion. First, we extract the difference co-arrays (DCA) from SDCA and construct the co-array interpolation model via nuclear norm minimization to initialize the virtual uniform rectangular array (URA) that does not contain the entire rows and columns of holes. Then, we utilize the shift-invariance structure of the virtual URA to construct the enhanced matrix with a two-fold Hankel structure to fill the remaining empty elements. More importantly, we apply the alternating direction method of the multipliers (ADMM) framework to solve the enhanced matrix completion model. To reduce the computational complexity of the traditional vector-form, sparse recovery algorithm caused by the Kronecker product operation between dictionary matrices, we derive a complex-valued sparse matrix-recovery model based on the fast iterative shrinkage-thresholding (FISTA) method. Finally, simulation results demonstrate the effectiveness of the proposed algorithm.

Parallel Greedy Search for Random Access in Wireless Networks

We consider the random access problem in wireless networks such as cellular networks and massive machine type communication networks, where a large number of devices/users are connected to a base station. In order to establish communication with the base station, as a part of the random access procedure, active users select and transmit codes (pilot sequences) randomly from a codebook. Since the active users are typically a small fraction of the total users, sparse signal recovery algorithms are employed to detect the transmitted codes. In this paper, we use multiple measurement vector model for the received signal and develop a parallel greedy search algorithm and it’s stopping criteria to detect the active users. We show through simulations that the proposed scheme, compared with the existing greedy algorithms, gives better detection performance at lower false alarms levels. We study how the code length and the code word size need to be chosen in order to detect a given number of active users. We also address the scenario when there are different timing offsets for signals received from different users.

Performance measure for sparse recovery algorithms in compressed sensing perspective

Performance measure for sparse recovery algorithms in compressed sensing perspective