Total variation with automatic hyper-parameter estimation

Medical diagnosis is often hampered by the quality of the images. This happens in a wide range of image modalities. Image noise reduction is a crucial step, however difficult to be accomplished. Bayesian algorithms have been commonly used with success, namely with additive white Gaussian noise (AWGN) model. In fact, the noise corrupting some of the most used medical imaging modalities is not additive neither Gaussian but multiplicative described by Poisson or Rayleigh distributions. This paper proposes a unified framework with automatic hyper parameters estimation. The proposed framework deals with AWGN but also with both Poisson and Rayleigh distributions. The algorithm proposed herein, is based on a maximum a posteriori (MAP) criterion with the edge preserving prior based on the total variation (TV), which avoids the distortion of relevant anatomical details. The denoising technique is performed via single parametric iterative scheme parameterized for each noise model considered. Tests with real data from several medical imaging modalities testify the performance of the algorithm.