Applications of Anisotropic Multiple Multiresolution Analyses

The concept of multiple multiresolution analysis (MMRA) generalizes the standard wavelet analysis and synthesis technique, in the sense that at each level the filterbank makes use of several scaling matrices and pairs of low-pass/high-pass filters chosen from finite given sets. This approach allows, in the 2D case, for a better detection of directional singularities in images, in particular when sets of anisotropic scaling matrices are employed. In this talk we present many examples illustrating the effectiveness of several multiple multiresolution analyses based on appropriate choices of scaling matrices and corresponding filters [1,2] when applied to some image processing problems, where compression and detection capabilities of the overall system are specifically required.