Quantized Sparse Approximation with Iterative Thresholding for Audio Coding

Sparse coding is a new field in signal processing with possible applications to source coding. In this paper we present a new method that combines the problems of sparse signal approximation with coefficient quantization. This method uses overcomplete dictionaries and exploits signal redundancy. The proposed method will be derived as an extension of a recently presented method (iterative thresholding) to find sparse representations of signals. Because in digital communication and storage we need a quantized representation of the signal, instead of quantization of sparse representations a posteriori, we propose a refined method that combines sparse approximation and quantization. To compare the proposed method to a posteriori quantization, we present an audio example.