SRF: Matrix Completion Based on Smoothed Rank Function

Hooshang Ghasemi (1) , Mohammadreza Malek-Mohammadi (1) , Massoud Babaie-Zadeh (1) , Christian Jutten (2)

1 EE department of SUT [Tehran] - Department of Electrical Engineering [Tehran]
2 GIPSA-VIBS - GIPSA - Vision and Brain Signal Processing

In this paper, we address the matrix completion problem and propose a novel algorithm based on a smoothed rank function (SRF) approximation. Among available algorithms like FPCA and OptSpace, there is no solution that can simultaneously cover wide range of easy and hard problems. This new algorithm provides accurate results in almost all scenarios with a reasonable run time. It especially has low execution time in hard problems where other methods need long time to converge. Furthermore, when the rank is known in advance and is high, our method is very faster than previous methods for the same accuracy. The main idea of the algorithm is based on a continuous and differentiable approximation of the rank function and then, using gradient projection approach to minimize it.

Mots clés: Sparse Signal Processing; Matrix completion; nuclear norm; Compressed Sensing

Domaines: Traitement du signal et de l'image [eess.SP]; Traitement du signal et de l'image [eess.SP]

Hooshang Ghasemi, Mohammadreza Malek-Mohammadi, Massoud Babaie-Zadeh, Christian Jutten. SRF: Matrix Completion Based on Smoothed Rank Function. ICASSP 2011 - IEEE International Conference on Acoustics, Speech and Signal Processing, May 2011, Prague, Czech Republic. pp.3672-3675. ⟨hal-00596777⟩