%0 Journal Article
%T Aiding Dictionary Learning Through Multi-Parametric Sparse Representation
%J Algorithms | An Open Access Journal from MDPI
%D 2019
%R https://doi.org/10.3390/a12070131
%X The £¿ 1 relaxations of the sparse and cosparse representation problems which appear in the dictionary learning procedure are usually solved repeatedly (varying only the parameter vector), thus making them well-suited to a multi-parametric interpretation. The associated constrained optimization problems differ only through an affine term from one iteration to the next (i.e., the problem¡¯s structure remains the same while only the current vector, which is to be (co)sparsely represented, changes). We exploit this fact by providing an explicit, piecewise affine with a polyhedral support, representation of the solution. Consequently, at runtime, the optimal solution (the (co)sparse representation) is obtained through a simple enumeration throughout the non-overlapping regions of the polyhedral partition and the application of an affine law. We show that, for a suitably large number of parameter instances, the explicit approach outperforms the classical implementation. View Full-Tex
%U https://www.mdpi.com/1999-4893/12/7/131