A Scale Invariant Bayesian Method to Solve Linear Inverse Problems

摘要: In this paper we propose a new Bayesian estimation method to solve linear inverse problems in signal and image restoration reconstruction which has the property be scale invariant. general, estimators are nonlinear functions of observed data. The only exception is Gaussian case. When dealing with linearity sometimes too strong property, while invariance often remains desirable property. As everybody knows one main difficulties using approach real applications assignment direct (prior) probability laws before applying Bayes’ rule. We discuss here how choose prior obtain invariant estimators. family generalized exponential distributions for probabilities (the p(x) likelihood p(y|x)), posterior p(x|y), and, consequently, Among many properties, exponentials can considered as maximum entropy subject knowledge finite set expectation values some known functions.