On deconvolution problems: numerical aspects

  • Authors:

  • Alexander G. Ramm;Alexandra B. Smirnova

  • Affiliations:

  • Department of Mathematics, Kansas State University, Manhattan, KS;Department of Mathematics and Statistics, Georgia State University, 30 Pryor Street, Atlanta, GA

  • Venue:
  • Journal of Computational and Applied Mathematics
  • Year:
  • 2005

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Abstract

An optimal algorithm is described for solving the deconvolution problem of the form ku := ∫01 k(t-s)u(s) ds = f(t) given the noisy data fδ,||f - fδ||≤δ. The idea of the method consists of the representation 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.