Maximum entropy signal restoration from short data records

There has been much discussion in the literature on the merits of the maximum entropy method arising from its information minimizing and consistency properties. In this paper we describe an application of the technique of the restoration of continuous signals given a set of sparsely sampled, noisy data. We compare the performance of the two common forms of the entropy cost functional, ? f ln (f) and ? ln (f), with an L_2 minimization. The deconvolution problem is formulated as the estimation of a continuous, unknown positive function given a discrete set of noisy samples i.e. a discrete-continuous formulation. Optimizing a cost functional on the solution subject to constraints derived from our prior knowledge of the problem allows us to select a unique solution from the generally infinite set of possible solutions, provide certain convexity requirements are fulfilled. Optimization is performed using a conjugate gradient method, the optimal step lengths were found using a Fibonacci search. Results demonstrate that use of the discrete-continuous MEM formulation allows the recovery or continuous signals from very short data records.