Fast Thresholding Algorithms with Feedbacks and Partially Known Support for Compressed Sensing

2020 ◽  
Vol 37 (03) ◽  
pp. 2050013
Author(s):  
Kaiyan Cui ◽  
Zhanjie Song ◽  
Ningning Han
Keyword(s):  
Numerical Experiments ◽  
Prior Information ◽  
Null Space ◽  
Sufficient Conditions ◽  
Sparse Signal Recovery ◽  
Sparse Signals ◽  
Signal Recovery ◽  
Hard Thresholding ◽  
Property Condition ◽  
Approximate Reconstruction

Some works in modified compressive sensing (CS) show that reconstruction of sparse signals can obtain better results than traditional CS using the partially known support. In this paper, we extend the idea of these works to the null space tuning algorithm with hard thresholding, feedbacks ([Formula: see text]) and derive sufficient conditions for robust sparse signal recovery. The theoretical analysis shows that including prior information of partially known support relaxes the preconditioned restricted isometry property condition comparing with the [Formula: see text]. Numerical experiments demonstrate that the modification improves the performance of the NST+HT+FB, thereby requiring fewer samples to obtain an approximate reconstruction. Meanwhile, a systemic comparison with different methods based on partially known support is shown.

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.

Sparse signal recovery with prior information by iterative reweighted least squares algorithm

2018 ◽  
Vol 26 (2) ◽  
pp. 171-184 ◽  
Author(s):  
Nianci Feng ◽  
Jianjun Wang ◽  
Wendong Wang
Keyword(s):  
Least Squares ◽  
Numerical Experiments ◽  
Prior Information ◽  
Regularization Parameter ◽  
Convergence Result ◽  
Sparse Signal ◽  
Sparse Signal Recovery ◽  
Signal Recovery ◽  
Recovery Performance ◽  
Iterative Reweighted Least Squares

AbstractIn this paper, the iterative reweighted least squares (IRLS) algorithm for sparse signal recovery with partially known support is studied. We establish a theoretical analysis of the IRLS algorithm by incorporating some known part of support information as a prior, and obtain the error estimate and convergence result of this algorithm. Our results show that the error bound depends on the best {(s+k)}-term approximation and the regularization parameter λ, and convergence result depends only on the regularization parameter λ. Finally, a series of numerical experiments are carried out to demonstrate the effectiveness of the algorithm for sparse signal recovery with partially known support, which shows that an appropriate q ({0<q<1}) can lead to a better recovery performance than that of the case {q=1}.

scholarly journals A Note on Block-Sparse Signal Recovery with Coherent Tight Frames

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Yao Wang ◽  
Jianjun Wang ◽  
Zongben Xu
Keyword(s):  
Sufficient Conditions ◽  
Tight Frame ◽  
Sparse Signal ◽  
Sparse Signal Recovery ◽  
Sparse Signals ◽  
Tight Frames ◽  
Signal Recovery ◽  
Analysis Method ◽  
Measurement Matrix ◽  
Undersampled Data

This note discusses the recovery of signals from undersampled data in the situation that such signals are nearly block sparse in terms of an overcomplete and coherent tight frameD. By introducing the notion of blockD-restricted isometry property (D-RIP), we establish several sufficient conditions for the proposed mixedl2/l1-analysis method to guarantee stable recovery of nearly block-sparse signals in terms ofD. One of the main results of this note shows that if the measurement matrix satisfies the blockD-RIP with constantsδk<0.307, then the signals which are nearly blockk-sparse in terms ofDcan be stably recovered via mixedl2/l1-analysis in the presence of noise.

scholarly journals Sparse signal recovery with multiple prior information: Algorithm and measurement bounds

2018 ◽  
Vol 152 ◽  
pp. 417-428
Author(s):  
Huynh Van Luong ◽  
Nikos Deligiannis ◽  
Jürgen Seiler ◽  
Søren Forchhammer ◽  
André Kaup
Keyword(s):  
Prior Information ◽  
Sparse Signal ◽  
Sparse Signal Recovery ◽  
Signal Recovery

scholarly journals Sparse Signal Recovery via ECME Thresholding Pursuits

2012 ◽  
Vol 2012 ◽  
pp. 1-22 ◽  
Author(s):  
Heping Song ◽  
Guoli Wang
Keyword(s):  
Optimization Problems ◽  
Greedy Algorithms ◽  
Experimental Studies ◽  
Superior Performance ◽  
Sparse Signal ◽  
Sparse Signal Recovery ◽  
Sparse Signals ◽  
Signal Recovery ◽  
Support Set ◽  
Reconstructed Signal

The emerging theory of compressive sensing (CS) provides a new sparse signal processing paradigm for reconstructing sparse signals from the undersampled linear measurements. Recently, numerous algorithms have been developed to solve convex optimization problems for CS sparse signal recovery. However, in some certain circumstances, greedy algorithms exhibit superior performance than convex methods. This paper is a followup to the recent paper of Wang and Yin (2010), who refine BP reconstructions via iterative support detection (ISD). The heuristic idea of ISD was applied to greedy algorithms. We developed two approaches for accelerating the ECME iteration. The described algorithms, named ECME thresholding pursuits (EMTP), introduced two greedy strategies that each iteration detects a support setIby thresholding the result of the ECME iteration and estimates the reconstructed signal by solving a truncated least-squares problem on the support setI. Two effective support detection strategies are devised for the sparse signals with components having a fast decaying distribution of nonzero components. The experimental studies are presented to demonstrate that EMTP offers an appealing alternative to state-of-the-art algorithms for sparse signal recovery.

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