Generalised information theory for inverse problems in signal processing

A powerful technique for the solution of a number of experimental inverse problems, described by an underlying first-kind Fredholm equation is presented. Such problems include, for example, diffraction-limited imaging and the analysis of laser light scattering data. The technique requires the construction of the 'singular system' of the problem which then provides exact orthonormal bases both for the description of sampled and truncated measured data and for the reconstructed continuous object 'solution' of the inversion. The singular-system approach may be regarded as a theory of information which generalizes in several directions the well known classical concepts of Shannon and Nyquist.SCOPUS: ar.j