Iterative Algorithms for Optimal Signal Reconstruction and Parameter Identification Given Noisy and Incomplete Data.

摘要

Presented is a new approach to the problem of estimating multiple unknown signals and/or parameters from noisy and incomplete data. The various unknowns are stochastically independent, then fitted into separable probability density approximation to the given model density by minimizing the cross-entropy. Given the separable density, all the unknowns can then be estimated independently of each other using conventional methods. Surprisingly, all the well known Maximum A Posteriori and Maximum Likelihood methods for this problem can be viewed as degenerate forms of this cross-entropy approach, in which one or more components of the fitted separable density are constrained to be impulse functions. The Minimum Cross-Entropy and MAP separable density approximations by iteratively minimizing with respect to each unknown component of the density are solved. This iterative approach takes a particularly simple form when the probability densities belong to an exponential class of densities. Each iteration decreases the cross-entropy, and convergence can be proven under mild conditions.