Entropy-Based Non-Local Means Filter for Single-Look SAR Speckle Reduction

Speckle is an interference phenomenon that contaminates images captured by coherent illumination systems. Due to its multiplicative and non-Gaussian nature, it is challenging to eliminate. The non-local means approach to noise reduction has proven flexible and provided good results. We propose in this work a new non-local means filter for single-look speckled data using the Shannon and Rényi entropies under the G0 model. We obtain the necessary mathematical apparatus (the Fisher information matrix and asymptotic variance of maximum likelihood estimators). The similarity between samples of the patches relies on a parametric statistical test that verifies the evidence whether two samples have the same entropy or not. Then, we build the convolution mask by transforming the p-value into weights with a smooth activation function. The results are encouraging, as the filtered images have a better signal-to-noise ratio, they preserve the mean, and the edges are not severely blurred. The proposed algorithm is compared with three successful filters: SRAD (Speckle Reducing Anisotropic Diffusion), Lee, and FANS (Fast Adaptive Nonlocal SAR Despeckling), showing the new method’s competitiveness.