Mutual information regularized Bayesian framework for multiple image restoration

Bayesian methods have been extensively used in various applications. However, there are two intrinsic issues rarely addressed, namely generalization and validity, in the context of multiple image restoration, we show that traditional Bayesian methods are sensitive to model errors and cannot guarantee valid results satisfying the underlying prior knowledge, e.g. independent noise property. To improve the Bayesian framework's generalization, we propose to explicitly enforce the validity of the result. Independent noise prior is very important but largely under-utilized in previous literature. In this paper, we use mutual information (MI) to explicitly enforce the independence. Efficient approximations based on Taylor expansion are proposed to adapt MI into standard energy forms to regularize the Bayesian methods. The new regularized Bayesian framework effectively utilizes the traditional generative signal/noise models but is much more robust to various model errors, as demonstrated in experiments on some demanding imaging applications.