A tight wavelet frame is a natural generation of an orthonormal wavelet if redundancy is introduced into the wavelet system. By allowing redundancy, we gain the necessary flexibility to achieve such properties as symmetry and, more importantly, the short support and high vanishing moments of compactly supported wavelets. In addition, redundancy allows for the approximate shift invariance behavior caused by the dense time-scale plane. We show some applications of symmetric tight wavelet frames (STWFs) for image processing, particularly image fusion, image denoising and image inpainting, and we demonstrate the possibility of using an STWF-based approach for such applications.
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