This book revolves around the question of designing a matrix D∈ Rm× n called dictionary,
such that to obtain good sparse representations y≈ Dx for a class of signals y∈ Rm given …

A dictionary learning problem is a matrix factorization in which the goal is to factorize a
training data matrix, Y, as the product of a dictionary, D, and a sparse coefficient matrix, X, as …

Modeling data with linear combinations of a few elements from a learned dictionary has
been the focus of much recent research in machine learning, neuroscience, and signal …

Sparse signal representation, analysis, and sensing have received a lot of attention in recent
years from the signal processing, optimization, and learning communities. On one hand …

We study in this thesis a particular machine learning approach to represent signals that that
consists of modelling data as linear combinations of a few elements from a learned …

The synthesis-based sparse representation model for signals has drawn considerable
interest in the past decade. Such a model assumes that the signal of interest can be …

Sparse coding---that is, modelling data vectors as sparse linear combinations of basis
elements---is widely used in machine learning, neuroscience, signal processing, and …

Many techniques in computer vision, machine learning, and statistics rely on the fact that a
signal of interest admits a sparse representation over some dictionary. Dictionaries are …

In recent years there has been a growing interest in the study of sparse representation of
signals. Using an overcomplete dictionary that contains prototype signal-atoms, signals are …

The power of sparse signal modeling with learned overcomplete dictionaries has been
demonstrated in a variety of applications and fields, from signal processing to statistical …