Microlocal filtering with multiwavelets

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Hyperfunctions in R^n are intuitively considered as sums of boundary values of holomorphic functions defined in infinitesimal wedges in C^n. Microlocal analysis corresponds the direction of analyticity of hyperfunctions to the direction of exponential decay of their Fourier transforms. Orthonormal multiwavelets, which are a generalization of orthonormal single wavelets, generate a multiresolution analysis by means of several scaling functions. Filtering is one of numerical methods and play central roles in digital image processing. We propose a multiwavelet system adapted to microlocal filtering. The main results are the following.A rough estimate of the microlocal content of functions or signals is obtained from their multiwavelet expansions.A fast algorithm for multiwavelet microlocal filtering is presented.Several numerical examples in digital image processing are considered.