A graph cut method for linear inverse problems

Abstract

In this paper we propose a graph cut method for solving a multi-label linear inverse problem with an arbitrary system matrix. Graph cuts are efficient methods for solving pixel-labeling and early vision problems. Energy function minimization problems that occur in image denoising are easily solved by graph cut techniques. However, applying graph cuts to inverse problems which have a non-diagonal system matrix becomes challenging, as a data cost of one pixel depends on intensities of other pixels. Such cost functions are not graph representable. In this paper, we propose an iterative method for minimization of energy functions occurring in inverse problems, where a graph-representable Taylor approximation of the original cost function is rapidly solved via a graph cut method at each iteration.