Image filtering by gradient inverse inhomogeneous diffusion

A method is developed for the synthesis of a nonlinear adaptive filter based on solutions to the inhomogeneous diffusion equation. The approach is based on the specification of the first derivative of the signal in time (scale). A general solution is derived and is then specialized to the scale invariance case, in which the diffusion coefficient is shown to be the gradient inverse. A novel discrete realization of the inhomogeneous diffusion equation is developed for the noise removal problem, and experimental results are shown. The proposed algorithm not only removes noise but simultaneously enhances and localizes edges. It is extremely simple and parallel, and does not require the detection of any of the many possible line and edge configurations. Since the algorithm is sensitive to the local context, it satisfies human vision requirements more than conventional methods which rely on minimizing the mean square error.<>