Variance Stabilizing Transformations in Patch-Based Bilateral Filters for Poisson Noise Image Denoising

Denoising is a key step in the processing of medical images. It aims at improving both the interpretability and visual aspect of the images. Yet, designing a robust and efficient denoising tool remains an unsolved challenge and a specific issue concerns the noise model. Many filters typically assume that noise is additive and Gaussian, with uniform variance. In contrast, noise in medical images often has more complex properties. This paper considers images with Poissonian noise and the patch-based bilateral filters, that is, filters that involve a tonal kernel and pair wise comparisons between shifted blocks of the images. The main aim is then to integrate two variance stabilizing transformations that allow the filters to work with Gaussianized noise. The performances of these filters are compared to those of the classical bilateral filter with the same transformations. The experiments include an artificial benchmark as well as a positron emission tomography image.