A new iterated two-band diffusion equation: Theory and its application

In this paper, we propose an iterated two-band filtering method to solve the selective image smoothing problem. We prove that a discrete computation step in an iterated nonlinear diffusion-based filtering algorithm is equivalent to a sequence of operations, including decomposition, regularization, and then reconstruction, in the proposed two-band filtering scheme. To correctly separate the high frequency components from the low frequency ones in the decomposition process, we adopt a dyadic wavelet-based approximation, scheme. In the regularization process, we use a diffusivity function as a guide to retain, useful data and suppress noises. Finally, the signal of the next stage, which is a "smoother" version of the signal at the previous stage, can be computed by reconstructing the decomposed low frequency component and the regularized high frequency component. Based on the proposed scheme, the smoothing operation can be applied to the correct targets. Experimental results show that our new approach is really efficient in noise removing.