Iterative mix thresholding algorithm with continuation technique for mix sparse optimization and application

Mix sparse structure is inherited in a wide class of practical applications, namely, the sparse structure appears as the inter-group and intra-group manners simultaneously. In this paper, we propose an iterative mix thresholding algorithm with continuation technique (IMTC) to solve the ℓ 0 regulariz...

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Vydáno v:Journal of global optimization Ročník 91; číslo 3; s. 511 - 534
Hlavní autoři: Hu, Yaohua, Lu, Jian, Yang, Xiaoqi, Zhang, Kai
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York Springer US 01.03.2025
Springer Nature B.V
Témata:
Absorption spectroscopy
Algorithms
Computer Science
Convergence
Mathematics
Mathematics and Statistics
Misalignment
Noise levels
Noise tolerance
Operations Research/Decision Theory
Optimization
Real Functions
Iterative thresholding algorithm
Mix sparse optimization
Regularization
Continuation technique
Convergence theory
ISSN:0925-5001, 1573-2916
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Shrnutí:Mix sparse structure is inherited in a wide class of practical applications, namely, the sparse structure appears as the inter-group and intra-group manners simultaneously. In this paper, we propose an iterative mix thresholding algorithm with continuation technique (IMTC) to solve the ℓ 0 regularized mix sparse optimization. The significant advantage of the IMTC is that it has a closed-form expression and low storage requirement, and it is able to promote the mix sparse structure of the solution. We prove the convergence property and the linear convergence rate of the ITMC to a local minimum; moreover, we show that the ITMC approaches an approximate true mix sparse solution within a tolerance relevant to the noise level under an assumption of restricted isometry property. We also apply the mix sparse optimization to model the differential optical absorption spectroscopy analysis with the wavelength misalignment, and numerical results indicate that the IMTC can exactly and quantitatively predict the existing materials and the factual wavelength misalignment simultaneously within 0.1 s, which meets the demand of improvement of the automatic analysis software.
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ISSN:0925-5001
1573-2916
DOI:10.1007/s10898-024-01441-w