Dynamic pattern denoising method using multi-basin system with kernels

In this paper, we propose a novel pattern denoising method that utilizes the topological property of a support that describes the distribution of normal patterns to denoise noisy patterns. The method first trains a support function which captures the domain of normal patterns and then construct a so-called multi-basin system associated with the trained support function. By moving noisy patterns along the trajectories of the multi-basin system, noise is removed while the pattern recovers its normality. The denoised pattern is obtained when the noisy pattern arrives at the attracting manifold generated by a set of normal patterns and this is the most similar normal pattern with the noisy pattern in the topological sense. Through simulations on some toy dataset and real image datasets, we show that the proposed framework effectively removes the noise while preserving the information contained in the noisy pattern.