Dyadic wavelet-based nonlinear conduction equation: theory and applications

We proposed a new dyadic wavelet-based conduction approach to take the place of the nonlinear diffusion equation for selective image smoothing. We also proved that the proposed iterated system always satisfies the so-called maximum-minimum principle no matter what kind of wavelet basis is used. Since the proposed approach does not require one to solve a partial differential equation (PDE), it is therefore more efficient and accurate than the conventional nonlinear diffusion/conduction-based methods. Experimental results using 1-D synthetic data and a real image demonstrated that the proposed method can efficiently remove noise and preserve real data.