scholarly journals Splitting Matching Pursuit Method for Reconstructing Sparse Signal in Compressed Sensing

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
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.

scholarly journals A Novel Coherence Reduction Method in Compressed Sensing for DOA Estimation

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Jing Liu ◽  
ChongZhao Han ◽  
XiangHua Yao ◽  
Feng Lian
Keyword(s):  
Compressed Sensing ◽  
Phased Array ◽  
Reduction Method ◽  
Doa Estimation ◽  
Estimation Methods ◽  
Sensing Matrix ◽  
Replacement Method ◽  
Precise Estimation ◽  
Novel Method ◽  
Measurement Vector

A novel method named as coherent column replacement method is proposed to reduce the coherence of a partially deterministic sensing matrix, which is comprised of highly coherent columns and random Gaussian columns. The proposed method is to replace the highly coherent columns with random Gaussian columns to obtain a new sensing matrix. The measurement vector is changed accordingly. It is proved that the original sparse signal could be reconstructed well from the newly changed measurement vector based on the new sensing matrix with large probability. This method is then extended to a more practical condition when highly coherent columns and incoherent columns are considered, for example, 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, where the compressed sensing method based on the original sensing matrix fails. The proposed method also obtains more precise estimation of DOA using one snapshot compared with the traditional estimation methods such as Capon, APES, and GLRT, based on hundreds of snapshots.

scholarly journals Constrained Backtracking Matching Pursuit Algorithm for Image Reconstruction in Compressed Sensing

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.

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

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.

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

2013 ◽  
pp. 125-138
Author(s):  
Chun-Yan Zeng ◽  
Li-Hong Ma ◽  
Ming-Hui Du ◽  
Jing Tian
Keyword(s):  
Compressed Sensing ◽  
Compressive Sensing ◽  
Matching Pursuit ◽  
Greedy Algorithms ◽  
Diagrammatic Representation ◽  
Support Set ◽  
Exact Reconstruction ◽  
Signal Characteristics ◽  
Sparsity Level

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.

Array DOA Estimation by the Model of Four Elements in Quare Array Based on the Theory of Compressed Sensing

2014 ◽  
Vol 635-637 ◽  
pp. 971-977 ◽  
Author(s):  
Rui Yuan ◽  
Jun Yue ◽  
Hong Xiu Gao
Keyword(s):  
Computer Simulation ◽  
Computational Complexity ◽  
Compressed Sensing ◽  
Matching Pursuit ◽  
Doa Estimation ◽  
Low Computational Complexity ◽  
Matching Pursuit Algorithm ◽  
Square Array

The DOA estimation by the model of four elements in the square array has studied based on the theory of compressed sensing. Using matching pursuit algorithm and orthogonality matching pursuit algorithm, the computer simulation was presented. The results show the method of DOA estimation by compressed sensing theory is simple, practical and low computational complexity.

REMARKS ABOUT ORTHOGONAL MATCHING PURSUIT ALGORITHMS

2012 ◽  
Vol 04 (04) ◽  
pp. 1250026 ◽  
Author(s):  
ZHIQIANG XU
Keyword(s):  
Compressed Sensing ◽  
Large Class ◽  
Matching Pursuit ◽  
Orthogonal Matching Pursuit ◽  
Sparse Signal ◽  
Instance Optimality

The orthogonal matching pursuit (OMP) is a popular decoder to recover sparse signal in compressed sensing. Our aim is to investigate the theoretical properties of OMP. In particular, we show that the OMP decoder can give (p, q) instance optimality for a large class of encoders with 1 ≤ p ≤ q ≤ 2 and (p, q) ≠ (2, 2).

A Modifying Sub-Threshold Weak Conjugate Gradient Pursuit Method

2012 ◽  
Vol 155-156 ◽  
pp. 191-195
Author(s):  
Zhi Yuan Yang ◽  
Jian Ping Li ◽  
En Ming Dong
Keyword(s):  
Compressed Sensing ◽  
Conjugate Gradient ◽  
Least Square Method ◽  
Least Square ◽  
Sparse Signal ◽  
Stopping Criterion ◽  
Sparsity Level

A modifying Sub-threshold Weak Conjugate Gradient Pursuit Method is proposed to improve recovery accuracy of Compressed Sensing. This method adds a direction in the Directional Pursuit Method and uses a stopping criterion for the indices of elements, then the evaluation of sparse signal is obtained by using Least Square Method. The simulation shows that for the same sparsity level, the number of measurements needed by the method is less than that needed by MP or StOMP-FDR to exactly recover, and the recovery accuracy is higher.

scholarly journals Tree-Based Backtracking Orthogonal Matching Pursuit for Sparse Signal Reconstruction

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Yigang Cen ◽  
Fangfei Wang ◽  
Ruizhen Zhao ◽  
Lihong Cui ◽  
Lihui Cen ◽  
...  
Keyword(s):  
Compressed Sensing ◽  
Optimization Problem ◽  
Selection Process ◽  
Matching Pursuit ◽  
Signal Reconstruction ◽  
Search Space ◽  
Orthogonal Matching Pursuit ◽  
Superior Performance ◽  
Sparse Signal ◽  
Tree Model

Compressed sensing (CS) is a theory which exploits the sparsity characteristic of the original signal in signal sampling and coding. By solving an optimization problem, the original sparse signal can be reconstructed accurately. In this paper, a new Tree-based Backtracking Orthogonal Matching Pursuit (TBOMP) algorithm is presented with the idea of the tree model in wavelet domain. The algorithm can convert the wavelet tree structure to the corresponding relations of candidate atoms without any prior information of signal sparsity. Thus, the atom selection process will be more structural and the search space can be narrowed. Moreover, according to the backtracking process, the previous chosen atoms’ reliability can be detected and the unreliable atoms can be deleted at each iteration, which leads to an accurate reconstruction of the signal ultimately. Compared with other compressed sensing algorithms, simulation results show the proposed algorithm’s superior performance to that of several other OMP-type algorithms.

scholarly journals A Two-Step Compressed Sensing Approach for Single-Snapshot DOA Estimation of Closely Spaced Signals

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Shuang Wei ◽  
Yanhua Long ◽  
Rui Liu ◽  
Ying Su
Keyword(s):  
Compressed Sensing ◽  
Doa Estimation ◽  
Estimation Methods ◽  
Estimation Accuracy ◽  
Accurate Estimation ◽  
Measurement Matrix ◽  
Chaotic Sequences ◽  
Overcomplete Dictionary ◽  
Highly Correlated ◽  
Single Snapshot

Single-snapshot direction-of-arrival (DOA) estimation plays an important role in dynamic target detection and tracking applications. Because a single-snapshot signal provides few information for statistics calculation, recently compressed sensing (CS) theory is applied to solve single-snapshot DOA estimation, instead of the traditional DOA methods based on statistics. However, when the unknown sources are closely located, the spatial signals are highly correlated, and its overcomplete dictionary is made up of dense grids, which leads to a serious decrease in the estimation accuracy of the CS-based algorithm. In order to solve this problem, this paper proposed a two-step compressed sensing-based algorithm for the single-snapshot DOA estimation of closely spaced signals. The overcomplete dictionaries with coarse and refined grids are used in the two steps, respectively. The measurement matrix is constructed by using a very sparse projection scheme based on chaotic sequences because chaotic sequences have determinism and pseudo-randomness property. Such measurement matrix is mainly proposed for compressing the overcomplete dictionary in preestimation step, while it is well designed by choosing the steering vectors of true DOA in the accurate estimation step, in which the neighborhood information around the true DOAs partly solved in the previous step will be used. Monte Carlo simulation results demonstrate that the proposed algorithm can perform better than other existing single-snapshot DOA estimation methods. Especially, it can work well to solve the issues caused by closely spaced signals and single snapshot.

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