Data Modeling: Visual Psychology Approach and <font>L</font><sub>1/2</sub> Regularization Theory

Xu, Zongben

doi:10.1142/9789814324359_0184

Cited by 32 publications

(25 citation statements)

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“…The sparsity of the L q (1/2 ≤ q < 1) solution increases as q decreases, whereas the sparsity of the solution for L q (0 < q ≤ 1/2) shows little change with respect to q [45], [46], making q = 1/2 a good regularizer choice. Moreover, when the full additivity constraint…”

Section: B Sparsity Analysismentioning

confidence: 99%

Hyperspectral Unmixing via $L_{1/2}$ Sparsity-Constrained Nonnegative Matrix Factorization

Qian

Jia

Zhou

et al. 2011

IEEE Trans. Geosci. Remote Sensing

506

451

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Hyperspectral unmixing is a crucial preprocessing step for material classification and recognition. In the last decade, nonnegative matrix factorization (NMF) and its extensions have been intensively studied to unmix hyperspectral imagery and recover the material end-members. As an important constraint for NMF, sparsity has been modeled making use of the L1 regularizer. Unfortunately, the L1 regularizer cannot enforce further sparsity when the full additivity constraint of material abundances is used, hence, limiting the practical efficacy of NMF methods in hyperspectral unmixing. In this paper, we extend the NMF method by incorporating the L 1/2 sparsity constraint, which we name L 1/2 -NMF. The L 1/2 regularizer not only induces sparsity, but is also a better choice among Lq(0 < q < 1) regularizers. We propose an iterative estimation algorithm for L 1/2 -NMF, which provides sparser and more accurate results than those delivered using the L1 norm. We illustrate the utility of our method on synthetic and real hyperspectral data and compare our results to those yielded by other state-of-the-art methods.

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Section: B Sparsity Analysismentioning

confidence: 99%

Hyperspectral Unmixing via $L_{1/2}$ Sparsity-Constrained Nonnegative Matrix Factorization

Qian

Jia

Zhou

et al. 2011

IEEE Trans. Geosci. Remote Sensing

506

451

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“…Although it accelerated the optimization procedure without the need of numerous iterations as required by the Newton-Raphson method, it still needed to compute and compare multiple roots using some discriminant rules. Cao, Xu, et al, [10,11,13] deduced the closed-form thresholding formulae in Equation (2.6) especially for p = 1/2 or 2/3 cases, which had a significant acceleration over Krishnan, et al's analytic solution. But if we try the same manipulation to p = 4/5, this results in a 6th order polynomial, which can only be solved numerically.…”

Section: W Sub-problemmentioning

confidence: 93%

“…Cao, Xu, et al, [10][11][12][13] deduced the closed-form thresholding formulae to solve and accelerated the algorithm. Based on their work, we extend the thresholding representation theory established on 1 / 2 regularization term to the cases with the combination of two norms, and deduce the closed-form thresholding formulae of the proposed algorithm in this paper.…”

Section: Closed-form Thresholding Formulamentioning

confidence: 99%

“…To improve the speed, Krishnan, et al, [5] proposed the analytic solution of image deconvolution based on p (p = 1/2; p = 2/3) regularization. Xu, et al, [10][11][12] deduced the closed-form thresholding formula of the ℓ 1/2 regularization model, and exhibited a fast, iterative, half-thresholding algorithm. Cao, et al, [13] presented the closed-form thresholding formula of the ℓ 2/3 regularization model, which not only got better results, but also sped up the algorithm of image deconvolution.…”

Section: Introductionmentioning

confidence: 99%

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A Non-Convex Approximating Norm Regularization Algorithm for Image Deconvolution

Liu¹,

Zhong²,

Jiang³

et al. 2016

IJSIP

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“…Flow Diagram of Proposed Algorithm deconvolution algorithm by using a closed-form threshold formula of l q regularization [28,29,30] which is very simple and fast.…”

Section: Image Recovery Via Split Methods and Closed-form Threshold Fomentioning

confidence: 99%

Concave–convex norm ratio prior based double model and fast algorithm for blind deconvolution

Peng

Gan

2016

Neurocomputing

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Data Modeling: Visual Psychology Approach and L_1/2 Regularization Theory

Cited by 32 publications

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Hyperspectral Unmixing via $L_{1/2}$ Sparsity-Constrained Nonnegative Matrix Factorization

Hyperspectral Unmixing via $L_{1/2}$ Sparsity-Constrained Nonnegative Matrix Factorization

A Non-Convex Approximating Norm Regularization Algorithm for Image Deconvolution

Concave–convex norm ratio prior based double model and fast algorithm for blind deconvolution

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Data Modeling: Visual Psychology Approach and L1/2 Regularization Theory

Cited by 32 publications

References 0 publications

Hyperspectral Unmixing via $L_{1/2}$ Sparsity-Constrained Nonnegative Matrix Factorization

Hyperspectral Unmixing via $L_{1/2}$ Sparsity-Constrained Nonnegative Matrix Factorization

A Non-Convex Approximating Norm Regularization Algorithm for Image Deconvolution

Concave–convex norm ratio prior based double model and fast algorithm for blind deconvolution

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Data Modeling: Visual Psychology Approach and L_1/2 Regularization Theory