On deconvolution problems: numerical aspects

2004/08/14 by А. Г. Рамм, Ramm, A. G., Alexandra Smirnova +1
Engineering · Mathematics · Medicine · #Algorithm #Applied mathematics #Calculus (dental) #Computer science #Deconvolution #Differential Equations and Boundary Problems #Heat Transfer and Mathematical Modeling #Mathematics #Medicine #Numerical methods in inverse problems #Orthodontics

paper · pdf · doi:10.48550/arxiv.math/0408195

published in arXiv (Cornell University) (Cornell University)

openalex publication_date 2004/08/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

An optimal algorithm is described for solving the deconvolution problem of the form \bf ku:=∫₀^tk(t-s)u(s)ds=f(t) given the noisy data f_δ, ||f-f_δ||≤ δ. The idea of the method consists of the representation \bf k=A(I+S), where S is a compact operator, I+S is injective, I is the identity operator, A is not boundedly invertible, and an optimal regularizer is constructed for A. The optimal regularizer is constructed using the results of the paper MR 40#5130.

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