Abstract
This article discusses a model for obtaining a sparse representation of a signal vector in ℝk, based on a system of linear equations with an orthogonal matrix. Such a representation minimizes a target function that combines the deviation from the exact solution and a chosen functional J. The functionals chosen are the Euclidean norm, the norm |⋅|1, and the quasi-norm |⋅|0. The Euclidean norm only allows for the exact solution, while the other two allow for a balance between the residual and the parameter λin the functional, resulting in sparser solutions. Graphs are plotted showing the dependence between the coordinates of the optimal vector and the parameter , and examples are provided.
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