Machine Learning

Chapter 9

Sparsity-Aware Learning

Concepts and Theoretical Foundations

Abstract

This chapter presents the main concepts and theoretical foundations related to sparsity-aware learning techniques. The concept of sparse modeling is introduced together with the LASSO and the ℓ₀ and ℓ₁ norm minimizing tasks. Conditions for uniqueness of the obtained solutions as well as for the equivalence of the ℓ₀ and ℓ₁ norm minimization are stated. The RIP condition and related bounds are discussed. Compressed sensing and the notion of stable embeddings are reviewed. The concept of sub-Nyquist sampling is presented and finally a case study concerning image de-nosing is reported.

Keywords

Sparse modeling

LASSO

Basis pursuit

ℓ₀ and ℓ₁ norms

Spark

Mutual coherence ...