Sparse Atomic Modeling of Audio: a Review
Research into sparse atomic models has recently intensified in the image and audio processing communities. While other reviews exist, we believe this paper provides a good starting point for the uninitiated reader as it concisely summarizes the state-of-the-art, and presents most of the major topics in an accessible manner. We discuss several approaches to the sparse approximation problem including various greedy algorithms, iteratively re-weighted least squares, iterative shrinkage, and Bayesian methods. We provide pseudo-code for several of the algorithms, and have released software which includes fast dictionaries and reference implementations for many of the algorithms. We discuss the relevance of the different approaches for audio applications, and include numerical comparisons. We also illustrate several audio applications of sparse atomic modeling.