Deep learned SVT: Unrolling singular value thresholding to obtain better MSE

TL;DR

This paper introduces a trainable deep neural network called Learned SVT that unrolls the singular value thresholding algorithm to improve matrix reconstruction accuracy and robustness in affine rank minimization problems.

Contribution

The paper presents a novel deep learning approach that unrolls SVT into a trainable network, achieving lower MSE and greater robustness compared to traditional SVT.

Findings

LSVT reconstructs matrices with lower MSE than traditional SVT.

LSVT is more robust to parameter selection than SVT.

Deep unrolling improves performance in affine rank minimization.

Abstract

Affine rank minimization problem is the generalized version of low rank matrix completion problem where linear combinations of the entries of a low rank matrix are observed and the matrix is estimated from these measurements. We propose a trainable deep neural network by unrolling a popular iterative algorithm called the singular value thresholding (SVT) algorithm to perform this generalized matrix completion which we call Learned SVT (LSVT). We show that our proposed LSVT with fixed layers (say T) reconstructs the matrix with lesser mean squared error (MSE) compared with that incurred by SVT with fixed (same T) number of iterations and our method is much more robust to the parameters which need to be carefully chosen in SVT algorithm.