Total Variation Differential Equation with Wavelet Transform for Image Restoration

To overcome the staircasing effects and simultaneously avoid edge blurring, we present an adaptive partial differential equation combining the total variation with wavelet transform for image restoration. A noise removal algorithm based on variation method and partial difference equations is proposed in this paper. The combining algorithm takes the advantage of both filters since it is able to preserve edges while avoiding the staircase effect in smooth regions. The TV method provides fast adaptive wavelet-based solvers for the TV model. Our approach not only employs a wavelet collocation method applied to the TV model using two-dimensional anisotropic tensor product of wavelets, but also proposes the differential equation for image restoration. Most conventional image processors consider little the influence of human vision psychology. The algorithm inherently not only combines the restoration property of wavelet compression algorithms with that of the TV model, but also gives a relative new TV functional which considers the influence of human vision psychology. We present a detailed description of our method which indicates that a combination of wavelet based restoration techniques with the TV model produces superior results. Experimental results illustrate the effectiveness of the model image restoration.