Inverse filtering and restoration of signals in noise

Abstract

One of the fundamental problems of signal processing is the restoration of an unknown signal. Restoration is based on a distorted version of the original signal mixed with noise; deterioration may originate due to passing through a distorting and noisy system (e.g. a communication channel). We will try to recover the original signal form from its measured (observed, received) deteriorated version on the basis of some knowledge of the properties (or mechanism) of deterioration. In the previous chapters, we have dealt with the question of how the signal will be changed by passing through a system. Now we are going to solve the inverse problem of finding the input, based on knowledge of the output, in the more general case also influenced by noise interference.