Multiscale representation of surfaces by tight wavelet frames with applications to denoising

In this paper, we introduce a new multiscale representation of surfaces using tight wavelet frames. Both triangular and quadrilateral (quad) surfaces are considered. The multiscale representation for triangulated surfaces is generalized from the non-tensor-product tight wavelet frame representation of functions (of two variables) that were introduced in [1], while the tensor-product tight frames of continuous linear B-spline from [63] are used for quad surfaces representation. As one of many possible applications of such representation, we consider surface denoising as an example at the end of the paper. We propose an analysis based surface denoising model for triangular and quad surfaces. Fast numerical algorithms are also proposed, which is different from the algorithms used in image restoration [50] and [52] due to the nonlinear nature of the proposed tight wavelet frame transforms on surfaces.