Year: 2023
Type: book-chapter
Abstract: The sparse modeling is an evident manifestation capturing the parsimony principle just described, and sparse models are widespread in statistics, physics, information sciences, neuroscience, computational mathematics, and so on. In statistics the many applications of sparse modeling span regression, classification tasks, graphical model selection, sparse M-estimators, and sparse dimensionality reduction. This chapter provides a brief introduction of the basic theory underlying sparse representation and compressive sensing and then discusses some methods for recovering sparse solutions to optimization problems in an effective way, together with some applications of sparse recovery in a machine learning problem known as sparse dictionary learning. Conditions on the mutual coherence can lead to the uniqueness and recoverability of the sparsest solution. Mutual coherence is easy to compute and give a lower bound to the spark. Many of the greedy algorithms proposed in literature for carrying out sparse recovery look for a linear expansion of the unknown signal s in terms of functions ϕ i .
Source: CRC Press eBooks
Author: Jianyi Lin
Institution: Università Cattolica del Sacro Cuore
Language: English
Subfield: Signal Processing
Field: Computer Science
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W4381333522