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Journal of Scientific Computing
Erschienen in: Journal of Scientific Computing 3/2023

01.06.2023

Study on \(L_1\) over \(L_2\) Minimization for Nonnegative Signal Recovery

verfasst von: Min Tao, Xiao-Ping Zhang

Erschienen in: Journal of Scientific Computing | Ausgabe 3/2023

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Abstract

In this paper, we carry out a comprehensive study for the unconstrained \(L_1\) over \(L_2\) sparsity promoting model, widely used in the regime of coherent dictionaries for recovering nonnegative sparse signals. First, we prove the existence of global solutions. Second, we analyze the sparse property of any local minimizer of the \(L_{1}/L_{2}\) model. This property serves as a certificate to rule out the nonlocal minimizers. Third, we focus on algorithmic development on the unconstrained model with nonnegative constraint. We derive an analytical solution for the proximal operator of the \(L_{1} / L_{2}\) with nonnegative constraint. Then, we apply the alternating direction method of multipliers in a particular splitting way, referred to as ADMM\(_p^+\). We establish its global convergence to a d-stationary solution (sharpest stationary) by verifying the Lyapunov function with the Kurdyka-Łojasiewicz property instead of imposing. Extensive numerical simulations confirm the superiority of ADMM\(_p^+\) over the existing state-of-the-art methods in nonnegative sparse recovery.
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Fußnoten
1
The original SOOT algorithm proposed in [29] aims to solve blind deconvolution, i.e., finding the unknown signal and blur simultaneously.
 
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Metadaten
Titel
Study on over Minimization for Nonnegative Signal Recovery
verfasst von
Min Tao
Xiao-Ping Zhang
Publikationsdatum
01.06.2023
Verlag
Springer US
Erschienen in
Journal of Scientific Computing / Ausgabe 3/2023
Print ISSN: 0885-7474
Elektronische ISSN: 1573-7691
DOI
https://doi.org/10.1007/s10915-023-02225-2

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