Maximum Entropy Criteria Applied to Signal Recovery

摘要

A method based on the minimization of cross-entropy is presented for the recovery of signals from noisy data either in the form of time series or images. Finite Fourier transforms are applied to the data and constraints are placed on the magnitude and phase of the Fourier coefficients based on their statistics for noise-only data. The minimization of cross-entropy is achieved through application of well-established functional minimization techniques which allow for further constraints in the spatial, temporal or frequency domain. Derivatives of the entropy function are obtained analytically and the results applied to the cases of correlated noise and of signal perturbations about a mean. Demonstrations of applications to one-dimensional data are presented. Keywords: Image processing; Maximum entropy methods; Signal recovery; Spatial analysis; and Signal processing; Canada. (rh)