Principal Basis Analysis in Sparse Representation

TL;DR

Principal basis analysis is a novel method for signal analysis that identifies reproducible sparse components to effectively extract underlying patterns from noisy data, improving denoising performance.

Contribution

It introduces a new criterion based on reproducibility for sparse component selection, enabling effective signal extraction and denoising.

Findings

Outperforms reference methods in image denoising tasks.

Effectively suppresses strong noise while preserving details.

Demonstrates the utility of reproducibility in sparse component analysis.

Abstract

This article introduces a new signal analysis method, which can be interpreted as a principal component analysis in sparse decomposition of the signal. The method, called principal basis analysis, is based on a novel criterion: reproducibility of component which is an intrinsic characteristic of regularity in natural signals. We show how to measure reproducibility. Then we present the principal basis analysis method, which chooses, in a sparse representation of the signal, the components optimizing the reproducibility degree to build the so-called principal basis. With this principal basis, we show that the underlying signal pattern could be effectively extracted from corrupted data. As illustration, we apply the principal basis analysis to image denoising corrupted by Gaussian and non-Gaussian noises, showing better performances than some reference methods at suppressing strong noise and at preserving signal details.