A Novel Sufficient Condition for Generalized Orthogonal Matching Pursuit

Wen, Jinming; Zhou, Zhengchun; Li, Dongfang; Tang, Xiaohu

doi:10.1109/lcomm.2016.2642922

Cited by 46 publications

(37 citation statements)

References 18 publications

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“…Two well-known and widely used scenarios in MMP, synthetic signal recovery and image reconstruction are performed to validate the acceleration effect of pruning tree strategy. The experiments are implemented via the accelerated MMP, in comparison with OMP, CoSaMP [17], SP [18], StOMP [19], gOMP [20], ROMP [21], A * OMP [22] and original MMP (MMP_BF). In our experiment, the measurement matrix ∈ R m×n (m = 100, n = 256) is taken from the Gaussian distribution N (1, 1 m ).…”

Section: Resultsmentioning

confidence: 99%

“…3) Finally, the pruning can be executed within the valid range. In fact, the condition (16) and (44) in [16] (or the condition (20) and (48) in [14]) guarantees the first two conditions, while…”

Section: A Analysis Of the Pruning Parameter Within The Valid Rangementioning

confidence: 99%

“…where (a) is from (15) and (b) is due to the facts that (I − [20]. On the other hand, after the K -th iterations, the minimal residual of the proposed algorithm is given by…”

Section: Appendix C Proof Of Theoremmentioning

confidence: 99%

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An Accelerated MMP With a Pruning Tree Strategy

Chen

Xiang

et al. 2019

IEEE Access

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Multipath matching pursuit (MMP) has been developed to solve the sparse signal recovery problems in compressed sensing, which can generate recovery error less than the traditional orthogonal matching pursuit type algorithms in terms of mean square error. However, the computational burden of MMP is seriously heavy, and limits itself in applications, finding the need to be improved urgently. To lighten the burden, in this paper, an accelerated version of the MMP is proposed based on pruning tree strategy for sparse signal recovery, that attempts to reduce some of the paths in subsequent searching. By this strategy, an accelerated MMP is established in the scenarios where the MMP works. It retains the desirable performance as MMP and can shorten the running time. We demonstrate the acceleration ability of the proposed algorithm with almost the same accuracy of the original MMP, for the reconstruction of both synthetic data and images. INDEX TERMS Compressed sensing, multipath matching pursuit, sparse recovery, pruning tree strategy, restricted isometry constant.

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Section: Resultsmentioning

confidence: 99%

Section: A Analysis Of the Pruning Parameter Within The Valid Rangementioning

confidence: 99%

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An Accelerated MMP With a Pruning Tree Strategy

Chen

Xiang

et al. 2019

IEEE Access

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“…One of the main technical challenges for CS is how to reduce the measurements, meanwhile, to obtain high-quality images. Typical applications of CS include radar imaging [2], channel estimation in communications systems [3][4][5][6], sparse recovery [7] and signal detection [8][9][10][11][12], electrocardiogram signal reconstruction [13], magnetic resonant imaging (MRI) [14][15][16], and especially in image processing [17][18][19].…”

Section: Introductionmentioning

confidence: 99%

Nonconvex Nonsmooth Low-Rank Minimization for Peneralized Image Compressed Sensing via Group Sparse Representation

Li¹,

Liu²,

Yu³

et al. 2020

Preprint

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Group sparse representation (GSR) based method has led to great successes in various image recovery tasks, which can be converted into a low-rank matrix minimization problem. As a widely used surrogate function of low-rank, the nuclear norm based convex surrogate usually leads to over-shrinking problem, since the standard soft-thresholding operator shrinks all singular values equally. To improve traditional sparse representation based image compressive sensing (CS) performance, we propose a generalized CS framework based on GSR model, which leads to a nonconvex nonsmooth low-rank minimization problem. The popular 2 -norm and M-estimator are employed for standard image CS and robust CS problem to fit the data respectively. For the better approximation of the rank of group-matrix, a family of nuclear norms are employed to address the over-shrinking problem. Moreover, we also propose a flexible and effective iteratively-weighting strategy to control the weighting and contribution of each singular value. Then we develop an iteratively reweighted nuclear norm algorithm for our generalized framework via an alternating direction method of multipliers framework, namely, GSR-AIR. Experimental results demonstrate that our proposed CS framework can achieve favorable reconstruction performance compared with current state-of-the-art methods and the robust CS framework can suppress the outliers effectively.

show abstract

“…One of the main technical challenges for CS is how to reduce the measurements whereas obtain high-quality images. Typical applications of CS include radar imaging [2], channel estimation in communications systems [3][4][5][6], sparse recovery [7] and signal detection [8][9][10][11][12], electrocardiogram signal reconstruction [13], magnetic resonant imaging (MRI) [14][15][16], and especially in image processing [17][18][19].…”

Section: Introductionmentioning

confidence: 99%

Nonconvex Nonsmooth Low-Rank Minimization for Peneralized Image Compressed Sensing via Group Sparse Representation

Li¹,

Liu²,

Yu³

et al. 2020

Preprint

View full text Add to dashboard Cite

Group sparse representation (GSR) based method has led to great successes in various image recovery tasks, which can be converted into a low-rank matrix minimization problem. As a widely used surrogate function of low-rank, the nuclear norm based convex surrogate usually leads to over-shrinking problem, since the standard soft-thresholding operator shrinks all singular values equally. To improve traditional sparse representation based image compressive sensing (CS) performance, we propose a generalized CS framework based on GSR model, leading to a nonconvex nonsmooth low-rank minimization problem. The popular -norm and M-estimator are employed for standard image CS and robust CS problem to fit the data respectively. For the better approximation of the rank of group-matrix, a family of nuclear norms are employed to address the over-shrinking problem. Moreover, we also propose a flexible and effective iteratively-weighting strategy to control the weighting and contribution of each singular value. Then we develop an iteratively reweighted nuclear norm algorithm for our generalized framework via an alternating direction method of multipliers framework, namely, GSR-ADMM-IRNN. Experimental results demonstrate that our proposed CS framework can achieve favorable reconstruction performance compared with current state-of-the-art methods and the RCS framework can suppress the outliers effectively.

show abstract

A Novel Sufficient Condition for Generalized Orthogonal Matching Pursuit

Cited by 46 publications

References 18 publications

An Accelerated MMP With a Pruning Tree Strategy

An Accelerated MMP With a Pruning Tree Strategy

Nonconvex Nonsmooth Low-Rank Minimization for Peneralized Image Compressed Sensing via Group Sparse Representation

Nonconvex Nonsmooth Low-Rank Minimization for Peneralized Image Compressed Sensing via Group Sparse Representation

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