2020/04/23 by Vincent Coppé, Coppé, Vincent, Daan Huybrechs +1
Computer Science · #FOS: Mathematics #Image and Signal Denoising Methods #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.2004.11317
openalex publication_date 2020/04/23 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
The approximation of smooth functions with a spectral basis typically leads\nto rapidly decaying coefficients where the rate of decay depends on the\nsmoothness of the function and vice-versa. The optimal number of degrees of\nfreedom in the approximation can be determined with relative ease by truncating\nthe coefficients once a threshold is reached. Recent approximation schemes\nbased on redundant sets and frames extend the applicability of spectral\napproximations to functions defined on irregular geometries and to certain\nnon-smooth functions. However, due to their inherent redundancy, the expansion\ncoefficients in frame approximations do not necessarily decay even for very\nsmooth functions. In this paper, we highlight this lack of equivalence between\nsmoothness and coefficient decay and we explore approaches to determine an\noptimal number of degrees of freedom for such redundant approximations.\n