Two-dimensional memory nonlinearities and their application to blind deconvolution problems

Blind deconvolution for a nonminimum phase linear time invariant system is possible only if some nonlinear estimates of the input or the higher-order statistics of the output are employed. When the convolutional noise is colored, the optimum estimates becomes memory nonlinear functions of the observations. Closed form solutions for the two-dimensional memory nonlinear MAP estimates depending on only the current observation and the immediately preceding one are derived for the following a priori probability density functions: (1) uniform, (2) Laplace and (3) exponential.<>