Multiplicative noise is often present in several medical and biological imaging modalities, such as MRI, Ultrasound, PET/SPECT and Fluorescence Microscopy. Noise removal and preserving the details is not a trivial task. Bayesian algorithms have been used to tackle this problem. They succeed to accomplish this task, however they lead to a computational burden as we increase the image dimensionality. Therefore, a significant effort has been made to accomplish this tradeoff, i.e., to develop fast and reliable algorithms to remove noise without distorting relevant clinical information. This paper provides a new unified framework for Bayesian denoising of images corrupted with additive and multiplicative noise. This allows to deal with additive white Gaussian and multiplicative noise described by Poisson and Rayleigh distributions respectively. The proposed algorithm is based on the maximum a posteriori (MAP) criterion, and an edge preserving priors are used to avoid the distortion of the relevant image details. The denoising task is performed by an iterative scheme based on Sylvester/Lyapunov equation. This approach allows to use fast and efficient algorithms described in the literature to solve the Sylvester/Lyapunov equation developed in the context of the Control theory. Experimental results with synthetic and real data testify the performance of the proposed technique, and competitive results are achieved when comparing to the of the state-of-the-art methods.
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