Synchronous Deautoconvolution of Positive Signals

DOI10.1016/J.CAM.2024.116025arXiv2302.12644MaRDI QIDQ6427529

Publication date: 24 February 2023

Abstract: We pose the problem of the optimal approximation of a given nonnegative signal

y_{t}

with the scalar autoconvolution

(x * x)_{t}

of a nonnegative signal

x_{t}

, where

x_{t}

and

y_{t}

are signals of equal length. The I-divergence has been adopted as optimality criterion, being well suited to incorporate nonnegativity constraints. To find a minimizer we derive an iterative descent algorithm of the alternating minimization type. The algorithm is based on the lifting of the original problem to a larger space, a relaxation technique developed by Csisz'ar and Tusn'adi which, in the present context, requires the solution of a hard partial minimization problem. We study the asymptotic behavior of the algorithm exploiting the optimality properties of the partial minimization problems and prove, among other results, that its limit points are Kuhn-Tucker points of the original minimization problem. Numerical experiments illustrate the results.

Mathematics Subject Classification ID

System identification (93B30) Measures of information, entropy (94A17)

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