PROJECT TITLE :

Local Kernels That Approximate Bayesian Regularization and Proximal Operators

ABSTRACT:

Kernel-based filtering, such as the bilateral filter and non-local means (as well as many others), is linked to broader variational formulations of Bayesian regularised least squares and the associated concept of proximal operators in this study. Optimization issues that cannot be solved in a closed form often arise from variational, Bayesian, or proximal formulations. Using locally adaptive filters with specified kernels, we show how one can estimate the solution of the ensuing global optimization problems. The approach is powerful enough to be useful for a wide range of applications because we expose how to derive a 'kernelized' solution to these problems that approximates the global solution in a single shot, using only local operations. Our results are valid for small regularisation strength (i.e., weak noise). Using a particular kernel decision in the construction of a local data-adaptive filter, we are able to analyse such filters in the variational/Bayesian/proximal framework.