Sparse Representations for Pattern Classification using Learned Dictionaries

Abstract

Sparse representations have been often used for inverse problems in signal and image processing. Furthermore, frameworks for signal classification using sparse and overcomplete representations have been developed. Data-dependent representations using learned dictionaries have been significant in applications such as feature extraction and denoising. In this paper, our goal is to perform pattern classification in a domain referred to as the data representation domain, where data from different classes are sparsely represented using an overcomplete dictionary. We propose a source model to characterize the data in each class and present an algorithm to infer the dictionary from the training data of all the classes. We estimate statistical templates in the data representation domain for each class of data, and perform classification using a likelihood measure. Simulation results show that, in the case of highly sparse signals, the proposed classifier provides a consistently good performance even under noisy conditions.