An Unconstrained $\ell_q$ Minimization with $0q\leq1$ for Sparse Solution of Underdetermined Linear Systems

Lai, Ming-Jun; Wang, Jingyue

doi:10.1137/090775397

Cited by 177 publications

(144 citation statements)

References 26 publications

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“…described above gaining in popularity in the literature (see, e.g., [7], [9], [14], [21], [23], [25], [27], [28]). However, there remains a key issue with respect to these choices: to what extent the minimizations (P p ) can achieve the same result as the initial minimization (P 0 ).…”

Section: Introductionmentioning

confidence: 99%

$NP/CMP$ Equivalence: A Phenomenon Hidden Among Sparsity Models $l_{0}$ Minimization and $l_{p}$ Minimization for Information Processing

Peng

Yue

2015

IEEE Trans. Inform. Theory

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Section: Introductionmentioning

confidence: 99%

$NP/CMP$ Equivalence: A Phenomenon Hidden Among Sparsity Models $l_{0}$ Minimization and $l_{p}$ Minimization for Information Processing

Peng

Yue

2015

IEEE Trans. Inform. Theory

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“…Based on the theoretical analysis in [20,26], both IRLS and IRL1 can guarantee to converge, while Chartland and Yin [12] showed that IRLS is theoretically better than IRL1. However, even for the simplest ℓ p -minimization problem in Eq.…”

Section: Related Workmentioning

confidence: 99%

A Generalized Iterated Shrinkage Algorithm for Non-convex Sparse Coding

Zuo

Meng

Zhang

et al. 2013

2013 IEEE International Conference on Computer Vision

311

196

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“…However, the study in the context of sparse signal recovery or compressed sensing has shown that L p norm (0 < p < 1) regularizations yield better solutions for sparse problems compared with L 1 norm. 11,12 Theoretical analysis and experimental results has proved that fewer measurements are enough for sparse signal recovery with L p regularization. Besides, the L 1=2 regularization has been recognized as a representative of L p (0 < p < 1).…”

Section: Introductionmentioning

confidence: 99%

Source reconstruction for bioluminescence tomography via L1∕2 regularization

2018

J. Innov. Opt. Health Sci.

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Bioluminescence tomography (BLT) is an important noninvasive optical molecular imaging modality in preclinical research. To improve the image quality, reconstruction algorithms have to deal with the inherent ill-posedness of BLT inverse problem. The sparse characteristic of bioluminescent sources in spatial distribution has been widely explored in BLT and many L 1 -regularized methods have been investigated due to the sparsity-inducing properties of L 1 norm. In this paper, we present a reconstruction method based on L 1=2 regularization to enhance sparsity of BLT solution and solve the nonconvex L 1=2 norm problem by converting it to a series of weighted L1 homotopy minimization problems with iteratively updated weights. To assess the performance of the proposed reconstruction algorithm, simulations on a heterogeneous mouse model are designed to compare it with three representative sparse reconstruction algorithms, including the weighted interior-point, L1 homotopy, and the Stagewise Orthogonal Matching Pursuit algorithm. Simulation results show that the proposed method yield stable reconstruction results under di®erent noise levels. Quantitative comparison results demonstrate that the proposed algorithm outperforms the competitor algorithms in location accuracy, multiple-source resolving and image quality.

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An Unconstrained $\ell_q$ Minimization with $0q\leq1$ for Sparse Solution of Underdetermined Linear Systems

Cited by 177 publications

References 26 publications

$NP/CMP$ Equivalence: A Phenomenon Hidden Among Sparsity Models $l_{0}$ Minimization and $l_{p}$ Minimization for Information Processing

$NP/CMP$ Equivalence: A Phenomenon Hidden Among Sparsity Models $l_{0}$ Minimization and $l_{p}$ Minimization for Information Processing

A Generalized Iterated Shrinkage Algorithm for Non-convex Sparse Coding

Source reconstruction for bioluminescence tomography via L1∕2 regularization

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