Regularization by Denoising for Inverse Problems in Imaging

Abstract

In this work, a generalized scheme of regularization of inverse problems is considered, where a priori knowledge about the smoothness of the solution is given by means of some self-adjoint operator in the solution space. The formulation of the problem is considered, namely, in addition to the main inverse problem, an additional problem is defined, in which the solution is the right-hand side of the equation. Thus, for the regularization of the main inverse problem, an additional inverse problem is used, which brings information about the smoothness of the solution to the initial problem. This formulation of the problem makes it possible to use operators of high complexity for regularization of inverse problems, which is an urgent need in modern machine learning problems, in particular, in image processing problems. The paper examines the approximation error of the solution of the initial problem using an additional problem.