Geodesic
On sparse approximations of solutions to linear systems with orthogonal matrices
Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, Tome 29 (2023) no. 1, pp. 7-14 Cet article a éte moissonné depuis la source Math-Net.Ru

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This article discusses a model for obtaining a sparse representation of a signal vector in $\mathbb{R}^k$, 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 $|\cdot|_1$, and the quasi-norm $|\cdot|_0$. The Euclidean norm only allows for the exact solution, while the other two allow for a balance between the residual and the parameter $\lambda$ in the functional, resulting in sparser solutions. Graphs are plotted showing the dependence between the coordinates of the optimal vector and the parameter $\lambda$, and examples are provided.
Keywords: sparse representations, objective function, minimization of the objective function, norms, pseudonorms, admissible error level. 
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A. V. Kiptenko; I. M. Izbiakov. On sparse approximations of solutions to linear systems with orthogonal matrices. Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, Tome 29 (2023) no. 1, pp. 7-14. http://geodesic.mathdoc.fr/item/VSGU_2023_29_1_a0/

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