On deconvolution problems: numerical aspects

An optimal algorithm is described for solving the deconvolution problem of the form ku≔∫0tk(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.