2012/01/12 by A. Krivoshein, Krivoshein, A.
Computer Science · Earth and Planetary Sciences · Mathematics · #42C40 #FOS: Mathematics #Functional Analysis (math.FA) #Image and Signal Denoising Methods #Mathematical Analysis and Transform Methods #Seismic Imaging and Inversion Techniques #math.FA #msc:42C40
paper · pdf · doi:10.48550/arxiv.1201.2606
arxiv created 2012/01/12 · openalex publication_date 2012/01/12 · arxiv updated 2012/01/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For an arbitrary matrix dilation, any integer n and any integer/semi-integer c, we describe all masks that are symmetric with respect to the point c and have sum rule of order n. For each such mask, we give explicit formulas for wavelet functions that are point symmetric/antisymmetric and generate frame-like wavelet system providing approximation order n. For any matrix dilations (which are appropriate for axial symmetry group on R2 in some natural sense) and given integer n, axial symmetric/antisymmetric frame-like wavelet systems providing approximation order n are constructed. Also, for several matrix dilations the explicit construction of highly symmetric frame-like wavelet systems providing approximation order n is presented.