An MMSE approach to nonlocal image denoising: Theory and practical implementation

A nonlocal minimum mean square error (MMSE) image denoising algorithm is proposed in this work. Based on the Bayesian estimation theory, we first derive that the conventional nonlocal means filter is an MMSE estimator in the special case of noise-free nonlocal neighbors. Then, we develop the nonlocal MMSE denoising filter that can minimize the mean square error (MSE) of a denoised block in more general cases of noisy nonlocal neighbors. Furthermore, the proposed algorithm searches nonlocal neighbors from an external database as well as the entire input image to improve the performance even when a noisy block may not have similar blocks within the image. Since the extended search range demands a higher computational burden, we develop a probabilistic tree-based search method to reduce the computational complexity. Simulation results show that the proposed algorithm provides significantly better denoising performance than the conventional nonlocal means filter.

► We propose a nonlocal denoising filter to minimize the MSE of a denoised block.
► The conventional NLM filter is optimal only if nonlocal neighbors are noise-free.
► Using an external database improves the denoising performance.