The Inverse Problem of Positive Autoconvolution

DOI10.1109/TIT.2023.3244407arXiv2111.14430OpenAlexW3214990587MaRDI QIDQ6199218

Lorenzo Finesso, Peter Spreij

Publication date: 21 March 2024

Published in: IEEE Transactions on Information Theory (Search for Journal in Brave)

Abstract: We pose the problem of approximating optimally a given nonnegative signal with the scalar autoconvolution of a nonnegative signal. The I-divergence is chosen as the optimality criterion being well suited to incorporate nonnegativity constraints. After proving the existence of an optimal approximation we derive an iterative descent algorithm of the alternating minimization type to find a minimizer. The algorithm is based on the lifting technique developed by Csisz'ar and Tusn'adi and exploits the optimality properties of the related minimization problems in the larger space. We study the asymptotic behavior of the iterative algorithm and prove, among other results, that its limit points are Kuhn-Tucker points of the original minimization problem. Numerical experiments confirm the asymptotic results and exhibit the fast convergence of the proposed algorithm.

Full work available at URL: https://arxiv.org/abs/2111.14430

zbMATH Keywords

inverse problemI-divergencepositive systemalternating minimizationautoconvolution

Mathematics Subject Classification ID

Information and communication theory, circuits (94-XX)

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Synchronous deautoconvolution algorithm for discrete-time positive signals via \(\mathcal{I}\)-divergence approximation

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