Parallel Dictionary Learning Algorithms for Sparse Representations

Sparse representations are intensively used in signal processing applications, like image coding, denoising, echo channels modeling, compression, classification and many others. Recent research has shown encouraging results when the sparse signals are created through the use of a learned dictionary. The current study focuses on finding new methods and algorithms, that have a parallel form where possible, for obtaining sparse representations of signals with improved dictionaries that lead to better performance in both representation error and execution time. We attack the general dictionary learning problem by first investigating and proposing new solutions for sparse representation stage and then moving on to the dictionary update stage where we propose a new parallel update strategy. Lastly, we study the effect of the representation algorithms on the dictionary update method. We also researched dictionary learning solutions where the dictionary has a specific form. We propose a new parallel algorithm for dictionaries structured as a union of orthonormal bases, we study and propose new methods when approaching the cosparse view on dictionary learning for the orthogonal case and, finally, we analyse and offer new algorithms for denosing with composite dictionaries.