Review of Sparsity Known and Blind Sparsity Greedy Algorithms for Compressed Sensing

Sparsity level is crucial to Compressive Sensing (CS) reconstruction, but in practice it is often unknown. Recently, several blind sparsity greedy algorithms have emerged to recover signals by exploiting the underlying signal characteristics. Sparsity Adaptive Matching Pursuit (SAMP) estimates the sparsity level and the true support set stage by stage, while Backtracking-Based Adaptive OMP (BAOMP) selects atoms by thresholds related to the maximal residual projection. This chapter reviews typical sparsity known greedy algorithms including OMP, StOMP, and CoSaMP, as well as those emerging blind sparsity greedy algorithms. Furthermore, the algorithms are analysed in structured diagrammatic representation and compared by exact reconstruction probabilities for Gaussian and binary signals distributed sparsely.

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Constrained Backtracking Matching Pursuit Algorithm for Image Reconstruction in Compressed Sensing

Applied Sciences ◽

10.3390/app11041435 ◽

2021 ◽

Vol 11 (4) ◽

pp. 1435

Author(s):

Xue Bi ◽

Lu Leng ◽

Cheonshik Kim ◽

Xinwen Liu ◽

Yajun Du ◽

...

Keyword(s):

Image Reconstruction ◽

Compressed Sensing ◽

Matching Pursuit ◽

Reconstruction Algorithm ◽

Energy Criterion ◽

Step Size ◽

Relationship Analysis ◽

Support Set ◽

Reconstruction Performance ◽

Sparsity Level

Image reconstruction based on sparse constraints is an important research topic in compressed sensing. Sparsity adaptive matching pursuit (SAMP) is a greedy pursuit reconstruction algorithm, which reconstructs signals without prior information of the sparsity level and potentially presents better reconstruction performance than other greedy pursuit algorithms. However, SAMP still suffers from being sensitive to the step size selection at high sub-sampling ratios. To solve this problem, this paper proposes a constrained backtracking matching pursuit (CBMP) algorithm for image reconstruction. The composite strategy, including two kinds of constraints, effectively controls the increment of the estimated sparsity level at different stages and accurately estimates the true support set of images. Based on the relationship analysis between the signal and measurement, an energy criterion is also proposed as a constraint. At the same time, the four-to-one rule is improved as an extra constraint. Comprehensive experimental results demonstrate that the proposed CBMP yields better performance and further stability than other greedy pursuit algorithms for image reconstruction.

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A Novel Sparse Data Reconstruction Algorithm for Dynamically Detect and Adjust Signal Sparsity

International Journal of Circuits, Systems and Signal Processing ◽

10.46300/9106.2021.15.61 ◽

2021 ◽

Vol 15 ◽

pp. 550-555

Author(s):

Dongxue Lu ◽

Zengke Wang

Keyword(s):

Matching Pursuit ◽

Greedy Algorithms ◽

Reconstruction Algorithm ◽

General Category ◽

Step Size ◽

Exact Reconstruction ◽

Matching Pursuit Algorithm ◽

The Right ◽

Sparsity Level ◽

Unknown Signal

This paper proposed a novel algorithm which is called the joint step-size matching pursuit algorithm (JsTMP) to solve the issue of calculating the unknown signal sparsity. The proposed algorithm falls into the general category of greedy algorithms. In the process of iteration, this method can adjust the step size and correct the indices of the estimated support that were erroneously selected in a dynamical way. And it uses the dynamical step sizes to increase the estimated sparsity level when the energy of the residual is less than half of that of the measurement vectory. The main innovations include two aspects: 1) The high probability of exact reconstruction, comparable to other classical greedy algorithms reconstruct arbitrary spare signal. 2) The sinh() function is used to adjust the right step with the value of the objective function in the late iteration. Finally, by following this approach, the simulation results show that the proposed algorithm outperforms state of- the-art similar algorithms used for solving the same problem.

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One-Bit Compressed Sensing by Greedy Algorithms

Numerical Mathematics Theory Methods and Applications ◽

10.4208/nmtma.2016.m1428 ◽

2016 ◽

Vol 9 (2) ◽

pp. 169-184 ◽

Cited By ~ 4

Author(s):

Wenhui Liu ◽

Da Gong ◽

Zhiqiang Xu

Keyword(s):

Compressed Sensing ◽

Greedy Algorithm ◽

Numerical Experiments ◽

Main Part ◽

Matching Pursuit ◽

Greedy Algorithms ◽

Orthogonal Matching Pursuit ◽

Sparse Signals

AbstractSign truncated matching pursuit (STrMP) algorithm is presented in this paper. STrMP is a new greedy algorithm for the recovery of sparse signals from the sign measurement, which combines the principle of consistent reconstruction with orthogonal matching pursuit (OMP). The main part of STrMP is as concise as OMP and hence STrMP is simple to implement. In contrast to previous greedy algorithms for one-bit compressed sensing, STrMP only need to solve a convex and unconstrained subproblem at each iteration. Numerical experiments show that STrMP is fast and accurate for one-bit compressed sensing compared with other algorithms.

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Signal Reconstruction Based on a Fusion Compressed Sensing Frame

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.785-786.1315 ◽

2013 ◽

Vol 785-786 ◽

pp. 1315-1323

Author(s):

Xu Hua Li ◽

Yue Li Chen ◽

Nan Jun Hu ◽

Wei Li ◽

Tian Jun Yuan ◽

...

Keyword(s):

Compressed Sensing ◽

Matching Pursuit ◽

Signal To Noise Ratio ◽

Signal Reconstruction ◽

Greedy Algorithms ◽

Reconstruction Error ◽

Reconstruction Accuracy ◽

Support Sets ◽

Reconstruction Effects ◽

Better Than

Greedy algorithms represented by orthogonal matching pursuit (OMP) and subspace pursuit (SP) algorithms are practically used in image processing based upon compressed sensing theory. However, there are two disadvantages: 1)Relatively poor signal reconstruction accuracy; 2) High computation complexity and measurements time. This paper proposes a frame of greedy algorithms obtaining a novel fusion of matching pursuit (FMP), combining the OMP and SP algorithms. FMP unites the two support sets from OMP and SP selecting the most appropriate atoms to achieve secondary screening of the original two support sets, finally realizing the accurate signal reconstruction. Using same test conditions, image reconstruction experiments and stability of Frame, the proposed FMP algorithm can effectively improve signal-to-noise ratio (SNR) with improved reconstruction error. Reconstruction effects using proposed FMP are better than separately using other two greedy algorithms for both high and low resolution images.

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Splitting Matching Pursuit Method for Reconstructing Sparse Signal in Compressed Sensing

Journal of Applied Mathematics ◽

10.1155/2013/804640 ◽

2013 ◽

Vol 2013 ◽

pp. 1-8 ◽

Cited By ~ 1

Author(s):

Liu Jing ◽

Han ChongZhao ◽

Yao XiangHua ◽

Lian Feng

Keyword(s):

Compressed Sensing ◽

Matching Pursuit ◽

Doa Estimation ◽

Estimation Methods ◽

Sparse Signal ◽

Ratio Test ◽

Correlation Vector ◽

Precise Estimation ◽

Novel Method ◽

Sparsity Level

In this paper, a novel method named as splitting matching pursuit (SMP) is proposed to reconstructK-sparse signal in compressed sensing. The proposed method selectsFl (Fl>2K)largest components of the correlation vectorc, which are divided intoFsplit sets with equal lengthl. The searching area is thus expanded to incorporate more candidate components, which increases the probability of finding the true components at one iteration. The proposed method does not require the sparsity levelKto be known in prior. The Merging, Estimation and Pruning steps are carried out for each split set independently, which makes it especially suitable for parallel computation. The proposed SMP method is then extended to more practical condition, e.g. the direction of arrival (DOA) estimation problem in phased array radar system using compressed sensing. Numerical simulations show that the proposed method succeeds in identifying multiple targets in a sparse radar scene, outperforming other OMP-type methods. The proposed method also obtains more precise estimation of DOA angle using one snapshot compared with the traditional estimation methods such as Capon, APES (amplitude and phase estimation) and GLRT (generalized likelihood ratio test) based on hundreds of snapshots.

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Compressed Sensing Image Reconstruction Based on Improved Particle Swarm Optimization Algorithm

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.599-601.1453 ◽

2014 ◽

Vol 599-601 ◽

pp. 1453-1456

Author(s):

Ju Wang ◽

Yin Liu ◽

Wei Juan Zhang ◽

Kun Li

Keyword(s):

Particle Swarm Optimization ◽

Image Reconstruction ◽

Compressed Sensing ◽

Optimization Algorithm ◽

Particle Swarm Optimization Algorithm ◽

Matching Pursuit ◽

Particle Swarm ◽

Premature Convergence ◽

Swarm Optimization ◽

Improved Particle Swarm Optimization

The reconstruction algorithm has a hot research in compressed sensing. Matching pursuit algorithm has a huge computational task, when particle swarm optimization has been put forth to find the best atom, but it due to the easy convergence to local minima, so the paper proposed a algorithm ,which based on improved particle swarm optimization. The algorithm referred above combines K-mean and particle swarm optimization algorithm. The algorithm not only effectively prevents the premature convergence, but also improves the K-mean’s local. These findings indicated that the algorithm overcomes premature convergence of particle swarm optimization, and improves the quality of image reconstruction.

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Filtering-Based Regularized Sparsity Variable Step-Size Matching Pursuit and Its Applications in Vehicle Health Monitoring

Applied Sciences ◽

10.3390/app11114816 ◽

2021 ◽

Vol 11 (11) ◽

pp. 4816

Author(s):

Haoqiang Liu ◽

Hongbo Zhao ◽

Wenquan Feng

Keyword(s):

Health Monitoring ◽

Matching Pursuit ◽

Signal Reconstruction ◽

Superior Performance ◽

Sparse Signal ◽

Variable Step Size ◽

Step Size ◽

Signal Sampling ◽

Reconstruction Performance ◽

Sparsity Level

Recent years have witnessed that real-time health monitoring for vehicles is gaining importance. Conventional monitoring scheme faces formidable challenges imposed by the massive signals generated with extremely heavy burden on storage and transmission. To address issues of signal sampling and transmission, compressed sensing (CS) has served as a promising solution in vehicle health monitoring, which performs signal sampling and compression simultaneously. Signal reconstruction is regarded as the most critical part of CS, while greedy reconstruction has been a research hotspot. However, the existing approaches either require prior knowledge of the sparse signal or perform with expensive computational complexity. To exploit the structure of the sparse signal, in this paper, we introduce an initial estimation approach for signal sparsity level firstly. Then, a novel greedy reconstruction algorithm that relies on no prior information of sparsity level while maintaining a good reconstruction performance is presented. The proposed algorithm integrates strategies of regularization and variable adaptive step size and further performs filtration. To verify the efficiency of the algorithm, typical voltage disturbance signals generated by the vehicle power system are taken as trial data. Preliminary simulation results demonstrate that the proposed algorithm achieves superior performance compared to the existing methods.

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