Please use this identifier to cite or link to this item:
http://hdl.handle.net/10397/93295
Title: | Analysis and algorithms for some compressed sensing models based on L1/L2 minimization | Authors: | Zeng, L Yu, P Pong, TK |
Issue Date: | 2021 | Source: | SIAM journal on optimization, 2021, v. 31, no. 2, p. 1576-1603 | Abstract: | Recently, in a series of papers [Y. Rahimi, C. Wang, H. Dong, and Y. Lou, SIAM J. Sci. Comput., 41 (2019), pp. A3649-A3672; C. Wang, M. Tao, J. Nagy, and Y. Lou, SIAM J. Imaging Sci., 14 (2021), pp. 749-777; C. Wang, M. Yan, and Y. Lou, IEEE Trans. Signal Process., 68 (2020), pp. 2660-2669; P. Yin, E. Esser, and J. Xin, Commun. Inf. Syst., 14 (2014), pp. 87-109], the ratio of \ell 1 and \ell 2 norms was proposed as a sparsity inducing function for noiseless compressed sensing. In this paper, we further study properties of such model in the noiseless setting, and propose an algorithm for minimizing \ell 1/\ell 2 subject to noise in the measurements. Specifically, we show that the extended objective function (the sum of the objective and the indicator function of the constraint set) of the model in [Y. Rahimi, C. Wang, H. Dong, and Y. Lou, SIAM J. Sci. Comput., 41 (2019), pp. A3649-A3672] satisfies the Kurdyka-\ Lojasiewicz (KL) property with exponent 1/2; this allows us to establish linear convergence of the algorithm proposed in [C. Wang, M. Yan, and Y. Lou, IEEE Trans. Signal Process., 68 (2020), pp. 2660-2669] (see equation 11) under mild assumptions. We next extend the \ell 1/\ell 2 model to handle compressed sensing problems with noise. We establish the solution existence for some of these models under the spherical section property [S. A. Vavasis, Derivation of Compressive Sensing Theorems from the Spherical Section Property, University of Waterloo, 2009; Y. Zhang, J. Oper. Res. Soc. China, 1 (2013), pp. 79-105] and extend the algorithm in [C. Wang, M. Yan, and Y. Lou, IEEE Trans. Signal Process., 68 (2020), pp. 2660-2669] (see equation 11) by incorporating moving-balls-approximation techniques [A. Auslender, R. Shefi, and M. Teboulle, SIAM J. Optim., 20 (2010), pp. 3232-3259] for solving these problems. We prove the subsequential convergence of our algorithm under mild conditions and establish global convergence of the whole sequence generated by our algorithm by imposing additional KL and differentiability assumptions on a specially constructed potential function. Finally, we perform numerical experiments on robust compressed sensing and basis pursuit denoising with residual error measured by \ell 2 norm or Lorentzian norm via solving the corresponding \ell 1/\ell 2 models by our algorithm. Our numerical simulations show that our algorithm is able to recover the original sparse vectors with reasonable accuracy. | Keywords: | Kurdyka-Lojasiewicz exponent L1/L2 minimization Linear convergence Moving balls approximation |
Publisher: | Society for Industrial and Applied Mathematics | Journal: | SIAM journal on optimization | ISSN: | 1052-6234 | EISSN: | 1095-7189 | DOI: | 10.1137/20M1355380 | Rights: | © 2021 Society for Industrial and Applied Mathematics The following publication Zeng, L., Yu, P., & Pong, T. K. (2021). Analysis and algorithms for some compressed sensing models based on L1/L2 minimization. SIAM Journal on Optimization, 31(2), 1576-1603 is available at https://doi.org/10.1137/20M1355380 |
Appears in Collections: | Journal/Magazine Article |
Files in This Item:
File | Description | Size | Format | |
---|---|---|---|---|
20m1355380.pdf | 532.52 kB | Adobe PDF | View/Open |
Page views
50
Last Week
0
0
Last month
Citations as of May 5, 2024
Downloads
73
Citations as of May 5, 2024
SCOPUSTM
Citations
12
Citations as of Apr 26, 2024
WEB OF SCIENCETM
Citations
11
Citations as of May 2, 2024
Google ScholarTM
Check
Altmetric
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.