Noise Level Estimation for Overcomplete Dictionary Learning Based on Tight Asymptotic Bounds

TL;DR

This paper introduces a statistically grounded method for accurately estimating Gaussian noise levels in overcomplete dictionary learning, leveraging eigenvalue distribution analysis and asymptotic bounds.

Contribution

It provides a novel interval-bounded estimator for noise variance that is theoretically justified and empirically validated in high-dimensional settings.

Findings

The estimator reliably infers true noise levels.

It outperforms existing noise estimation methods.

The approach is supported by rigorous eigenvalue distribution analysis.

Abstract

In this letter, we address the problem of estimating Gaussian noise level from the trained dictionaries in update stage. We first provide rigorous statistical analysis on the eigenvalue distributions of a sample covariance matrix. Then we propose an interval-bounded estimator for noise variance in high dimensional setting. To this end, an effective estimation method for noise level is devised based on the boundness and asymptotic behavior of noise eigenvalue spectrum. The estimation performance of our method has been guaranteed both theoretically and empirically. The analysis and experiment results have demonstrated that the proposed algorithm can reliably infer true noise levels, and outperforms the relevant existing methods.