Mol, ‘‘Generalised information theory for inverse problems in signal processing

Abstract: 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 generalises in several directions the well known classical concepts of Shannon and Nyquist.