Dictionary Subselection Using an Overcomplete Joint Sparsity Model

TL;DR

This paper introduces a novel exemplar-based method for selecting dictionaries in sparse signal representations, utilizing an overcomplete joint sparsity model to improve model selection for various signals.

Contribution

It proposes a new dictionary selection approach based on an overcomplete joint sparsity model, extending standard joint sparsity concepts for better signal modeling.

Findings

Effective in synthetic simulations

Applicable to realistic signal scenarios

Outperforms traditional dictionary selection methods

Abstract

Many natural signals exhibit a sparse representation, whenever a suitable describing model is given. Here, a linear generative model is considered, where many sparsity-based signal processing techniques rely on such a simplified model. As this model is often unknown for many classes of the signals, we need to select such a model based on the domain knowledge or using some exemplar signals. This paper presents a new exemplar based approach for the linear model (called the dictionary) selection, for such sparse inverse problems. The problem of dictionary selection, which has also been called the dictionary learning in this setting, is first reformulated as a joint sparsity model. The joint sparsity model here differs from the standard joint sparsity model as it considers an overcompleteness in the representation of each signal, within the range of selected subspaces. The new dictionary selection paradigm is examined with some synthetic and realistic simulations.