scholarly journals A New Generalized Orthogonal Matching Pursuit Method

2017 ◽  
Vol 2017 ◽  
pp. 1-7
Author(s):  
Liquan Zhao ◽  
Yulong Liu
Keyword(s):  
Matching Pursuit ◽  
High Reliability ◽  
Orthogonal Matching Pursuit ◽  
Sparse Signal ◽  
Sensing Matrix ◽  
Residual Vector ◽  
Reliability Indices ◽  
Support Set ◽  
Reconstruction Performance ◽  
Generalized Orthogonal

To improve the reconstruction performance of the generalized orthogonal matching pursuit, an improved method is proposed. Columns are selected from the sensing matrix by generalized orthogonal matching pursuit, and indices of the columns are added to the estimated support set to reconstruct a sparse signal. Those columns contain error columns that can reduce the reconstruction performance. Therefore, the proposed algorithm adds a backtracking process to remove the low-reliability columns from the selected column set. For any k-sparse signal, the proposed method firstly computes the correlation between the columns of the sensing matrix and the residual vector and then selects s columns that correspond to the s largest correlation in magnitude and adds their indices to the estimated support set in each iteration. Secondly, the proposed algorithm projects the measurements onto the space that consists of those selected columns and calculates the projection coefficient vector. When the size of the support set is larger than k, the proposed method will select k high-reliability indices using a search strategy from the support set. Finally, the proposed method updates the estimated support set using the selected k high-reliability indices. The simulation results demonstrate that the proposed algorithm has a better recovery performance.

scholarly journals A Sharp Bound on RIC in Generalized Orthogonal Matching Pursuit

2018 ◽  
Vol 61 (1) ◽  
pp. 40-54 ◽  
Author(s):  
Wengu Chen ◽  
Huanmin Ge
Keyword(s):  
Matching Pursuit ◽  
Natural Extension ◽  
Orthogonal Matching Pursuit ◽  
Sparse Signal ◽  
Sparse Signals ◽  
Sensing Matrix ◽  
Extra Condition ◽  
Exact Reconstruction ◽  
Restricted Isometry Constant ◽  
Generalized Orthogonal

AbstractThe generalized orthogonal matching pursuit (gOMP) algorithm has received much attention in recent years as a natural extension of the orthogonal matching pursuit (OMP). It is used to recover sparse signals in compressive sensing. In this paper, a new bound is obtained for the exact reconstruction of every K-sparse signal via the gOMP algorithm in the noiseless case. That is, if the restricted isometry constant (RIC) δNK+1 of the sensing matrix A satisfiesthen the gOMP can perfectly recover every K-sparse signal x from y = Ax. Furthermore, the bound is proved to be sharp. In the noisy case, the above bound on RIC combining with an extra condition on the minimum magnitude of the nonzero components of K-sparse signals can guarantee that the gOMP selects all of the support indices of the K-sparse signals.

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.

scholarly journals A Matching Pursuit Algorithm for Backtracking Regularization Based on Energy Sorting

Symmetry ◽  
2020 ◽  
Vol 12 (2) ◽  
pp. 231 ◽  
Author(s):  
Hanfei Zhang ◽  
Shungen Xiao ◽  
Ping Zhou
Keyword(s):  
Energy Distribution ◽  
Matching Pursuit ◽  
Signal Reconstruction ◽  
Selection Criterion ◽  
Critical Factor ◽  
Maximum Energy ◽  
Orthogonal Matching Pursuit ◽  
Support Set ◽  
Reconstruction Efficiency ◽  
Matching Pursuit Algorithm

The signal reconstruction quality has become a critical factor in compressed sensing at present. This paper proposes a matching pursuit algorithm for backtracking regularization based on energy sorting. This algorithm uses energy sorting for secondary atom screening to delete individual wrong atoms through the regularized orthogonal matching pursuit (ROMP) algorithm backtracking. The support set is continuously updated and expanded during each iteration. While the signal energy distribution is not uniform, or the energy distribution is in an extreme state, the reconstructive performance of the ROMP algorithm becomes unstable if the maximum energy is still taken as the selection criterion. The proposed method for the regularized orthogonal matching pursuit algorithm can be adopted to improve those drawbacks in signal reconstruction due to its high reconstruction efficiency. The experimental results show that the algorithm has a proper reconstruction.

Comparative Performance Evaluation of Greedy Algorithms for Speech Enhancement System

2020 ◽  
pp. 2150017
Author(s):  
Bittu Kumar
Keyword(s):  
Speech Enhancement ◽  
Matching Pursuit ◽  
Greedy Algorithms ◽  
Speech Quality ◽  
Orthogonal Matching Pursuit ◽  
Objective Measures ◽  
Comparative Performance ◽  
Perceptual Evaluation ◽  
Generalized Orthogonal ◽  
Recovery Algorithms

In this paper, the performance of compressive sensing (CS)-based technique for speech enhancement has been studied and results analyzed with recovery algorithms as a comparison of their performances. This is done for several recovery algorithms such as matching pursuit, orthogonal matching pursuit, stage-wise orthogonal matching pursuit, compressive sampling matching pursuit and generalized orthogonal matching pursuit. Performances of all these greedy algorithms were compared for speech enhancement. The evaluation of results has been carried out using objective measures (perceptual evaluation of speech quality, log-likelihood ratio, weighted spectral slope distance and segmental signal-to-noise ratio), simulation time and composite objective measures (signal distortion C[Formula: see text], background intrusiveness C[Formula: see text] and overall quality C[Formula: see text]. Results showed that the CS-based technique using generalized orthogonal matching pursuit algorithm yields better performance than the other recovery algorithms in terms of speech quality and distortion.

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