Nuclear norm and indicator function model for matrix completion

Juan Geng; Laisheng Wang; Xiuyu Wang

doi:10.1515/jiip-2013-0077

Published by De Gruyter May 21, 2015

Nuclear norm and indicator function model for matrix completion

Juan Geng , Laisheng Wang and Xiuyu Wang

From the journal Journal of Inverse and Ill-posed Problems

https://doi.org/10.1515/jiip-2013-0077

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Abstract

In the matrix completion problem, most methods to solve the nuclear norm model are relaxing it to the nuclear norm regularized least squares problem. In this paper, we propose a new unconstraint model for matrix completion problem based on nuclear norm and indicator function and design a proximal point algorithm (PPA-IF) to solve it. Then the convergence of our algorithm is established strictly. Finally, we report numerical results for solving noiseless and noisy matrix completion problems and image reconstruction.

Keywords: Matrix completion; nuclear norm; indicator function; proximal point algorithm

MSC: 90

Funding source: National Natural Science Foundation of China

Award Identifier / Grant number: 11271367

Received: 2013-12-10

Revised: 2014-6-11

Accepted: 2015-4-5

Published Online: 2015-5-21

Published in Print: 2016-2-1

Nuclear norm and indicator function model for matrix completion

Abstract

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