Nonlinear multigrid methods for total variation image denoising

Abstract

The classical image denoising technique introduced by Rudin, Osher, and Fatemi [17] a decade ago, leads to solve a constrained minimization problem for the total variation (TV) of the image. The formal first variation of the minimization problem is a nonlinear and highly anisotropic boundary value problem. In this paper, a computational PDE method based on a nonlinear multigrid scheme for restoring noisy images is suggested. Here, we examine different discretizations for the Euler---Lagrange equation as well as different smoothers within the multigrid scheme. Then we describe the iterative total variation regularization scheme, which starts with an isotropic ("smooth") problem and leads to smooth edges in the image. Within the iteration the problem becomes more and more anisotropic and converges to an image with sharp edges. Finally, we present some experimental results for synthetic and real images.