Removing multiplicative noise by improved regularization term

This paper focuses on the problem of multiplicative noise removal. Multiplicative noise models are central to the study of coherent imaging systems, such as synthetic aperture radar and sonar, and ultrasound and laser imaging. Classical ways to solve such problems are filtering, statistical(Bayesian) methods, variational methods, and methods that convert the multiplicative noise into additive noise, apply a variational method on the log data or shrink their coefficients in a frame and recover the result using an exponential function. We draw our inspiration from the diffusion tensor. By using a edge-directed enhancing based anisotropic diffusion as regularizer, we can derive a functional whose minimizer corresponds to the denoised image we want to recover. Both theory analysis and numerical results show that the new model has better denoising results than the known SO model with high peak signal to noise ratio.