On deconvolution problems: numerical aspects

An optimal algorithm is described for solving the deconvolution problem of the form k u ≔ ∫ 0 t k ( t - s ) u ( s ) d s = f ( t ) given the noisy data f δ , | | f - f δ | | ⩽ 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.