Summary: | 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi mathvariant="script">G</mi><mn>0</mn></msup></semantics></math></inline-formula> 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 <i>p</i>-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.
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