The Use of Singular Systems in Inverse Problems in Signal Processing

Abstract

In a number of experiments in various scientific fields a common method for determining certain characteristics of a physical sample is to observe the interaction between the sample and the radiation emitted by a known source. One or several detectors measure space and/or time variations of the scattered radiation, as scattering amplitudes, field fluctuations, absorption coefficients and so on. The output of the detectors can be digitized and the final result of the experiment is a set of (real or complex) numbers {gn}nN=1 stored in a computer. The interpretation of the data requires the solution of a mathematical problem, ie the restoration of the unknown characteristic of the sample from the set of numbers gn.