Robust Low-Rank Matrix Recovery as Mixed Integer Programming via \ell -norm Optimization

This letter focuses on the robust low-rank matrix recovery (RLRMR) in the presence of gross sparse outliers. Instead of using <inline-formula><tex-math notation="LaTeX">\ell _{1}</tex-math></inline-formula>-norm to reduce or suppress the influence of anomalies, we a...

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Bibliographic Details
Published in:IEEE signal processing letters Vol. 30; pp. 1 - 5
Main Authors: Shi, Zhang-Lei, Li, Xiao Peng, Li, Weiguo, Yan, Tongjiang, Wang, Jian, Fu, Yaru
Format: Journal Article
Language:English
Published: IEEE 01.08.2023
Subjects:
<inline-formula xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"> <tex-math notation="LaTeX"> ell _{0}</tex-math> </inline-formula>-norm optimization
binary optimization
Indexes
Integer programming
Manganese
mixed integer programming
Noise measurement
Optimization
Robust low-rank matrix recovery
Signal processing algorithms
Sparse matrices
ISSN:1070-9908, 1558-2361
Online Access:Get full text
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Summary:This letter focuses on the robust low-rank matrix recovery (RLRMR) in the presence of gross sparse outliers. Instead of using <inline-formula><tex-math notation="LaTeX">\ell _{1}</tex-math></inline-formula>-norm to reduce or suppress the influence of anomalies, we aim to eliminate their impact. To this end, we model the RLRMR as a mixed integer programming (MIP) problem based on the <inline-formula><tex-math notation="LaTeX">\ell _{0}</tex-math></inline-formula>-norm. Then, a block coordinate descent (BCD) algorithm is developed to iteratively solve the resultant MIP. At each iteration, the proposed approach first utilizes the <inline-formula><tex-math notation="LaTeX">\ell _{0}</tex-math></inline-formula>-norm optimization theory to assign binary weights to all entries of the residual between the known and estimated matrices. With these binary weights, the optimization over the bilinear term is reduced to a weighted extension of the Frobenius norm. As a result, the optimization problem is decomposed into a group of row-wise and column-wise subproblems with closed-form solutions. Additionally, the convergence of the proposed algorithm is studied. Simulation results demonstrate that the proposed method is superior to five state-of-the-art RLRMR algorithms.
ISSN:1070-9908
1558-2361
DOI:10.1109/LSP.2023.3301244