A dual space optimization technique for maximum entropy signal reconstruction and restoration

The properties of the maximum entropy method (MEM) as applied in digital signal processing have been the subject of much controversy in the recent literature. In this paper we attempt to clarify the properties of the MEM by considering statistical, Bayesian and model based interpretations. The modeling interpretation is based on a dual space optimization approach to the problem which allows the estimation of the unknown signal as a continuous function from a finite set of data. It is shown that the effective role of the entropy function is to select a model for the unknown signal of dimension equal to the number of data samples. This dual space approach is demonstrated in applications in signal deconvolution and image rcconstruction from projections using sparsely sampled, noisy data.