Universal Regularizers For Robust Sparse Coding and Modeling

TL;DR

This paper introduces a universal regularization framework for sparse coding based on codelength minimization, offering theoretical and practical improvements over traditional l0 and l1 regularizers in image processing tasks.

Contribution

It proposes a novel regularization approach derived from universal coding theory, enhancing sparse coding's effectiveness and robustness in signal and image processing.

Findings

Improved image denoising performance

Enhanced image zooming quality

Better classification accuracy

Abstract

Sparse data models, where data is assumed to be well represented as a linear combination of a few elements from a dictionary, have gained considerable attention in recent years, and their use has led to state-of-the-art results in many signal and image processing tasks. It is now well understood that the choice of the sparsity regularization term is critical in the success of such models. Based on a codelength minimization interpretation of sparse coding, and using tools from universal coding theory, we propose a framework for designing sparsity regularization terms which have theoretical and practical advantages when compared to the more standard l0 or l1 ones. The presentation of the framework and theoretical foundations is complemented with examples that show its practical advantages in image denoising, zooming and classification.