THE CONSTRUCTION OF MULTIWAVELET BI-FRAMES AND APPLICATIONS TO VARIATIONAL IMAGE DENOISING

Abstract

We remove noise from images by solving a parameter depending variational problem. The choice of the parameter is essential for the success of the approach, and in order to compute a solution, the problem must be discretized. It is commonly known that the parameter choice according to the H-curve criterion performs well in combination with discretizations derived from a dyadic orthonormal wavelet basis. However, the concept of orthonormal wavelet bases is restrictive and bears limitations. In order to have a more flexible tool, we construct new nondyadic wavelet bi-frames by convolving scalar wavelets with wavelet vectors. We discretize the variational problem by these new bi-frames, and we verify that the H-curve method performs well for this much more flexible discretization technique.