A Fast Data Driven Shrinkage of Singular Values for Arbitrary Rank Signal Matrix Denoising

TL;DR

This paper introduces a fast, data-driven singular value shrinkage method for low-rank matrix denoising that is computationally efficient and consistent with asymptotic optimal estimators, demonstrated on synthetic and real data.

Contribution

It proposes a non-iterative, data-dependent shrinkage function estimated via Stein's principle, improving speed and efficiency over existing methods.

Findings

The method achieves comparable denoising performance to asymptotically optimal estimators.

It significantly reduces computational complexity, enabling real-time applications.

Experimental results validate effectiveness on synthetic and magnetic resonance imaging data.

Abstract

Recovering a low-rank signal matrix from its noisy observation, commonly known as matrix denoising, is a fundamental inverse problem in statistical signal processing. Matrix denoising methods are generally based on shrinkage or thresholding of singular values with a predetermined shrinkage parameter or threshold. However, most of the existing adaptive shrinkage methods use multiple parameters to obtain a better flexibility in shrinkage. The optimal value of these parameters using either cross-validation or Stein's principle. In both the cases, the iterative estimation of various parameters render the existing shrinkage methods computationally latent for most of the real-time applications. This paper presents an efficient data dependent shrinkage function whose parameters are estimated using Stein's principle but in a non-iterative manner, thereby providing a comparatively faster shrinkage method. In addition, the proposed estimator is found to be consistent with the recently proposed asymptotically optimal estimators using the results from random matrix theory. The experimental studies on artificially generated low-rank matrices and on the magnetic resonant imagery data, show the efficacy of the proposed denoising method.