One-Step Deblurring and Denoising Color Images Using Partial Differential Equations

nonlinear diffusion filtering, deblurring, denoising An implicit, one-step method for the restoration of blurred and noisy color images is presented. Using a nonlinear partial differential equation (PDE)-based variational restoration approach, it is shown that a single iteration yields a result that is visually superior to performing Gaussian low-pass filtering, followed up by unsharp masking, a conventional linear process. The governing equation is constructed by examining ways to achieve the optimal balance between the two competitive forces, that of denoising and deblurring, at the same time. For the solution, the additive operator splitting (AOS) scheme is implemented, which allows the separation of spatial variables. A stable and efficient algorithm results from the decomposition of the problem, that has recently been developed for denoising without deblurring. Deblurring is added to denoising in such a way that the tridiagonal structure in each one of the dimensions is preserved, so that the algorithm remains inexpensive despite the matrix inversions. Results indicate that this one-step implementation yields a robust filter that can be tuned to preprocess images for various applications.