A New Nonlocal H 1 Model for Image Denoising

Abstract

Following ideas of Kindermann et al. (Multiscale Model. Simul. 4(4):1091---1115, 2005) and Gilboa and Osher (Multiscale Model. Simul. 7:1005---1028, 2008) we introduce new nonlocal operators to interpret the nonlocal means filter (NLM) as a regularization of the corresponding Dirichlet functional. Then we use these nonlocal operators to propose a new nonlocal H 1 model, which is (slightly) different from the nonlocal H 1 model of Gilboa and Osher (Multiscale Model. Simul. 6(2):595---630, 2007; Proc. SPIE 6498:64980U, 2007). The key point is that both the fidelity and the smoothing term are derived from the same geometric principle. We compare this model with the nonlocal H 1 model of Gilboa and Osher and the nonlocal means filter, both theoretically and in computer experiments. The experiments show that this new nonlocal H 1 model also provides good results in image denoising and closer to the nonlocal means filter than the H 1 model of Gilboa and Osher. This means that the new nonlocal operators yield a better interpretation of the nonlocal means filter than the nonlocal operators given in Gilboa and Osher (Multiscale Model. Simul. 7:1005---1028, 2008).