Denoising Magnetic Resonance Images Using Fourth Order Complex Diffusion

Complex diffusion is a comparatively new Partial Differential Equations (PDE) based method introduced for removing noise from images. The efficiency of 2^nd order complex diffusion for image denoising is already proved by many researchers. 2^nd order non linear complex diffusion can behave like 3^rd and 4^th order real PDEs enabling a variety of new options with standard 2^nd order numerical schemes. Extending 2^nd order non linear complex diffusion to 4^th order can produce a much better result. In this paper we present a 4^th order non linear complex diffusion. Our experimental results show that this 4^th order complex PDE is a good choice for denoising Magnetic Resonance images. The efficacy of the algorithm is demonstrated on both simulated and real magnetic resonance images.