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 2nd order complex diffusion for image denoising is already proved by many researchers. 2nd order non linear complex diffusion can behave like 3rd and 4th order real PDEs enabling a variety of new options with standard 2nd order numerical schemes. Extending 2nd order non linear complex diffusion to 4th order can produce a much better result. In this paper we present a 4th order non linear complex diffusion. Our experimental results show that this 4th 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.