The most ill-posed non-negative kernels in discrete deconvolution

Abstract

The author considers the Gauss-Markov formulation of the discrete convolution equation with noise. The ill-posedness of the problem depends on the kernel of the equation. The author characterises the most ill-posed kernels, which are almost the same for all linear deconvolution methods. He discusses them in detail for two methods. Recognising the most-ill posed kernels is a prerequisite for avoiding them or taking special action against them, e.g. by using a nonlinear method. The most ill-posed kernels are all similar to the binomial kernels, which are discretisations of the gaussian exp(-x²).