MAXIMUM-ENTROPY RECONSTRUCTION USING DERIVATIVE INFORMATION .1. FISHER INFORMATION AND CONVEX DUALITY

Maximum entropy spectral density estimation is a technique for reconst ructing an unknown density function from some known measurements by ma ximizing a given measure of entropy of the estimate. Here we present a variety of new entropy measures which attempt to control derivative v alues of the densities. Our models apply among others to the inference problem based on the averaged Fisher information measure. The duality theory we develop resembles models used in convex optimal control pro blems. We present a variety of examples, including relaxed moment matc hing with Fisher information and best interpolation on a strip.