scholarly journals Stochastic Gradient Matching Pursuit Algorithm Based on Sparse Estimation

Electronics ◽  
2019 ◽  
Vol 8 (2) ◽  
pp. 165 ◽  
Author(s):  
Liquan Zhao ◽  
Yunfeng Hu ◽  
Yulong Liu
Keyword(s):  
Prior Information ◽  
Matching Pursuit ◽  
Stochastic Gradient ◽  
Least Square ◽  
Improved Method ◽  
Step Size ◽  
Sparse Estimation ◽  
Practical Applications ◽  
Matching Pursuit Algorithm ◽  
Better Than

The stochastic gradient matching pursuit algorithm requires the sparsity of the signal as prior information. However, this prior information is unknown in practical applications, which restricts the practical applications of the algorithm to some extent. An improved method was proposed to overcome this problem. First, a pre-evaluation strategy was used to evaluate the sparsity of the signal and the estimated sparsity was used as the initial sparsity. Second, if the number of columns of the candidate atomic matrix was smaller than that of the rows, the least square solution of the signal was calculated, otherwise, the least square solution of the signal was set as zero. Finally, if the current residual was greater than the previous residual, the estimated sparsity was adjusted by the fixed step-size and stage index, otherwise we did not need to adjust the estimated sparsity. The simulation results showed that the proposed method was better than other methods in terms of the aspect of reconstruction percentage in the larger sparsity environment.

scholarly journals Improved Generalized Sparsity Adaptive Matching Pursuit Algorithm Based on Compressive Sensing

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Zhao Liquan ◽  
Ma Ke ◽  
Jia Yanfei
Keyword(s):  
Matching Pursuit ◽  
Initial Step ◽  
Convergence Speed ◽  
One Dimension ◽  
Measurement Matrix ◽  
Improved Method ◽  
Reconstruction Accuracy ◽  
Step Size ◽  
Matching Pursuit Algorithm ◽  
Initial Step Size

The modified adaptive orthogonal matching pursuit algorithm has a lower convergence speed. To overcome this problem, an improved method with faster convergence speed is proposed. In respect of atomic selection, the proposed method computes the correlation between the measurement matrix and residual and then selects the atoms most related to residual to construct the candidate atomic set. The number of selected atoms is the integral multiple of initial step size. In respect of sparsity estimation, the proposed method introduces the exponential function to sparsity estimation. It uses a larger step size to estimate sparsity at the beginning of iteration to accelerate the algorithm convergence speed and a smaller step size to improve the reconstruction accuracy. Simulations show that the proposed method has better performance in terms of convergence speed and reconstruction accuracy for one-dimension signal and two-dimension signal.

scholarly journals Improved Stochastic Gradient Matching Pursuit Algorithm Based on the Soft-Thresholds Selection

2018 ◽  
Vol 2018 ◽  
pp. 1-11
Author(s):  
Zhao Liquan ◽  
Hu Yunfeng
Keyword(s):  
Least Squares ◽  
Matching Pursuit ◽  
Signal Reconstruction ◽  
Stochastic Gradient ◽  
Selection Strategy ◽  
Index Set ◽  
Least Squares Solution ◽  
Matching Pursuit Algorithm ◽  
Sparsity Level ◽  
Better Than

The preliminary atom set exits redundant atoms in the stochastic gradient matching pursuit algorithm, which affects the accuracy of the signal reconstruction and increases the computational complexity. To overcome the problem, an improved method is proposed. Firstly, a limited soft-threshold selection strategy is used to select the new atoms from the preliminary atom set, to reduce the redundancy of the preliminary atom set. Secondly, before finding the least squares solution of the residual, it is determined whether the number of columns of the measurement matrix is smaller than the number of rows. If the condition is satisfied, the least squares solution is calculated; otherwise, the loop is exited. Finally, if the length of the candidate atomic index set is less than the sparsity level, the current candidate atom index set is the support atom set. If the condition is not satisfied, the support atom index set is determined by the least squares solution. Simulation results indicate that the proposed method is better than other methods in terms of the reconstruction probability and shorter running time than the stochastic gradient matching pursuit algorithm.

scholarly journals Endmember Learning with K-Means through SCD Model in Hyperspectral Scene Reconstructions

2019 ◽  
Vol 5 (11) ◽  
pp. 85 ◽  
Author(s):  
Ayan Chatterjee ◽  
Peter W. T. Yuen
Keyword(s):  
Dictionary Learning ◽  
Sparse Coding ◽  
Clustering Algorithm ◽  
Matching Pursuit ◽  
Orthogonal Matching Pursuit ◽  
Scene Reconstruction ◽  
Data Sets ◽  
Practical Applications ◽  
Input Dataset ◽  
Better Than

This paper proposes a simple yet effective method for improving the efficiency of sparse coding dictionary learning (DL) with an implication of enhancing the ultimate usefulness of compressive sensing (CS) technology for practical applications, such as in hyperspectral imaging (HSI) scene reconstruction. CS is the technique which allows sparse signals to be decomposed into a sparse representation “a” of a dictionary D u . The goodness of the learnt dictionary has direct impacts on the quality of the end results, e.g., in the HSI scene reconstructions. This paper proposes the construction of a concise and comprehensive dictionary by using the cluster centres of the input dataset, and then a greedy approach is adopted to learn all elements within this dictionary. The proposed method consists of an unsupervised clustering algorithm (K-Means), and it is then coupled with an advanced sparse coding dictionary (SCD) method such as the basis pursuit algorithm (orthogonal matching pursuit, OMP) for the dictionary learning. The effectiveness of the proposed K-Means Sparse Coding Dictionary (KMSCD) is illustrated through the reconstructions of several publicly available HSI scenes. The results have shown that the proposed KMSCD achieves ~40% greater accuracy, 5 times faster convergence and is twice as robust as that of the classic Spare Coding Dictionary (C-SCD) method that adopts random sampling of data for the dictionary learning. Over the five data sets that have been employed in this study, it is seen that the proposed KMSCD is capable of reconstructing these scenes with mean accuracies of approximately 20–500% better than all competing algorithms adopted in this work. Furthermore, the reconstruction efficiency of trace materials in the scene has been assessed: it is shown that the KMSCD is capable of recovering ~12% better than that of the C-SCD. These results suggest that the proposed DL using a simple clustering method for the construction of the dictionary has been shown to enhance the scene reconstruction substantially. When the proposed KMSCD is incorporated with the Fast non-negative orthogonal matching pursuit (FNNOMP) to constrain the maximum number of materials to coexist in a pixel to four, experiments have shown that it achieves approximately ten times better than that constrained by using the widely employed TMM algorithm. This may suggest that the proposed DL method using KMSCD and together with the FNNOMP will be more suitable to be the material allocation module of HSI scene simulators like the CameoSim package.

Least Support Orthogonal Matching Pursuit Algorithm With Prior Information

2014 ◽  
Vol 6 (2) ◽  
pp. 111-134 ◽  
Author(s):  
Israa Sh. Tawfic ◽  
Sema Koc Kayhan
Keyword(s):  
Numerical Experiments ◽  
Prior Information ◽  
Matching Pursuit ◽  
Recovery Process ◽  
Orthogonal Matching Pursuit ◽  
Sparse Signal Recovery ◽  
Sparse Signals ◽  
Signal Recovery ◽  
Reconstruction Performance ◽  
Matching Pursuit Algorithm

Abstract This paper proposes a new fast matching pursuit technique named Partially Known Least Support Orthogonal Matching Pursuit (PKLS-OMP) which utilizes partially known support as a prior knowledge to reconstruct sparse signals from a limited number of its linear projections. The PKLS-OMP algorithm chooses optimum least part of the support at each iteration without need to test each candidate independently and incorporates prior signal information in the recovery process. We also derive sufficient condition for stable sparse signal recovery with the partially known support. Result shows that inclusion of prior information weakens the condition on the sensing matrices and needs fewer samples for successful reconstruction. Numerical experiments demonstrate that PKLS-OMP performs well compared to existing algorithms both in terms of reconstruction performance and execution time.

scholarly journals Under-Determined Blind Source Separation

2021 ◽  
Author(s):  
Mehrdad Kafaiezadtehrani
Keyword(s):  
Blind Source Separation ◽  
Clustering Algorithm ◽  
Matching Pursuit ◽  
Source Separation ◽  
Least Square ◽  
Separation Problem ◽  
Second Stage ◽  
Mixing Matrix ◽  
Matching Pursuit Algorithm ◽  
Source Signals

The Under-determined Blind Source Separation problem aims at estimating N source signals, with only a given set of M known mixtures, where M < N. The problem is solved by a two-stage approach. The rst stage is the estimation of the unknown mixing matrix. The contributions made unravel a more precise and accurate tool which directly relates to the initialization of the clustering algorithm. Di erent schemes such as segmentation, correlation and least square curve tting are used to take advantage of the sparsity of the sources. A signi cant addition involves applying linear transforms to produce a higher sparse domain. Further, the second stage is the sparse source recovery using a Matching Pursuit algorithm. The contributions involve a Matching Pursuit algorithm with di

Sign in / Sign up

Export Citation Format

Share Document