New Improved Algorithms for Compressive Sensing Based on $\ell_{p}$ Norm

Pant, Jeevan K.; Lu, Wu-Sheng; Antoniou, A.

doi:10.1109/tcsii.2013.2296133

Cited by 63 publications

(56 citation statements)

References 12 publications

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“…First, we analyze the performance of the proposed RRCSFSL0 algorithm in sparse signal recovery, and compare it with the SL0 [31][32][33], L 2 -SL0 [27][28][29] and L p -RLS [26] algorithms. We fix n=256 and m=100 and the sparsity degree k=4s+1, s=1, 2, K, 15, or let n=[170, 220, 270, 320, 370, 420, 470, 520], m=n/2, k=n/5.…”

Section: Numerical Simulation and Analysismentioning

confidence: 99%

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A re-weighted smoothed L0 -norm regularized sparse reconstructed algorithm for linear inverse problems

Wang

Xiang

et al. 2019

J. Phys. Commun.

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This paper addresses the problems of sparse signal and image recovery using compressive sensing (CS), especially in the case of Gaussian noise. The main contribution of this paper is the proposal of the regularization re-weighted Composite Sine function smoothed L 0 -norm minimization (RRCSFSL0) algorithm where the Composite Sine function (CSF), the iteratively re-weighted scheme and the regularization mechanism represent the core of an approach to the solution of the problem. Compared with other state-of-the-art functions, the CSF we proposed can better approximate the L 0 -norm and improve the reconstruction accuracy, the new re-weighted scheme we adopted can promote sparsity and speed up convergence. Moreover, the use of the regularization mechanism makes the RRCSFSL0 algorithm more robust against noise. The performance of the proposed algorithm is verified via numerical experiments in the noise environment. Furthermore, experiments and comparisons demonstrate the superiority of the RRCSFSL0 algorithm in image restoration.

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Section: Numerical Simulation and Analysismentioning

confidence: 99%

“…Focal Underdetermined System Solver (FOCUSS) [22], Iterative Re-weighted Least Squares (IRLS) [23,24] and Bayesian CS (BCS) [25] are typical approaches to solve equation (4), which have rapid reconstruction speed, but are easy to fall into local optimum. [26] proposed a new algorithm called Lp-RLS, which converts…”

Section: Introductionmentioning

confidence: 99%

A re-weighted smoothed L0 -norm regularized sparse reconstructed algorithm for linear inverse problems

Wang

Xiang

et al. 2019

J. Phys. Commun.

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“…Many researchers have proposed the use of the p -norm for p < 1 as a better approximation for the 0 -norm, e.g., [33,38,48,49]. Smaller values of p result in better approximation; however, they result in an increase in the number of local optima, which either trap the algorithms in a suboptimal solution or translate into increased computational complexity.…”

Section: Sparse Spectral Unmixingmentioning

confidence: 99%

“…Smaller values of p result in better approximation; however, they result in an increase in the number of local optima, which either trap the algorithms in a suboptimal solution or translate into increased computational complexity. An alternative method is to iteratively reduce p from one to zero in order to take advantage of the unique optimal solution for p = 1 and then track the optimal solution for p < 1 as p is reducing [38]. The existing methods using the p -norm have a major drawback since for p < 1, the p -norm is not a Lipschitz continuous function.…”

Section: Sparse Spectral Unmixingmentioning

confidence: 99%

“…We gradually increase the parameter σ in order to allow the convergence and tracking of the best local optimal solution and iteratively find a better sparse solution. The arctan function is Lipschitz continuous; thus, the proposed method does not have additional considerations to avoid numerical problems, e.g., [25,37,38]. Moreover, our proposed algorithm improves the sparsity as σ varies from zero to ∞, whereas in [20,23], the value of σ is constant.…”

Section: Introductionmentioning

confidence: 99%

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ℓ0-Norm Sparse Hyperspectral Unmixing Using Arctan Smoothing

et al. 2016

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Abstract:The goal of sparse linear hyperspectral unmixing is to determine a scanty subset of spectral signatures of materials contained in each mixed pixel and to estimate their fractional abundances. This turns into an 0 -norm minimization, which is an NP-hard problem. In this paper, we propose a new iterative method, which starts as an 1 -norm optimization that is convex, has a unique solution, converges quickly and iteratively tends to be an 0 -norm problem. More specifically, we employ the arctan function with the parameter σ ≥ 0 in our optimization. This function is Lipschitz continuous and approximates 1 -norm and 0 -norm for small and large values of σ, respectively. We prove that the set of local optima of our problem is continuous versus σ. Thus, by a gradual increase of σ in each iteration, we may avoid being trapped in a suboptimal solution. We propose to use the alternating direction method of multipliers (ADMM) for our minimization problem iteratively while increasing σ exponentially. Our evaluations reveal the superiorities and shortcomings of the proposed method compared to several state-of-the-art methods. We consider such evaluations in different experiments over both synthetic and real hyperspectral data, and the results of our proposed methods reveal the sparsest estimated abundances compared to other competitive algorithms for the subimage of AVIRIS cuprite data.

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