| Abstract: |
| Approximation of functions from observed data is often needed. This has been widely studied in the literature when data is exact and the underlying function is smooth. However, the observed data is often contaminated with noise and the underlying function may be nonsmooth. To properly handle noisy and blurring data, any effective approximation scheme must contain a noise removal component. To well approximate nonsmooth functions, one needs to have a sparse approximation in, for example, the wavelet domain. This talk presents theoretical analysis and applications of such noise removal schemes through the lens of function approximation. For a given sample size, approximation from uniform grid data and scattered data is investigated. |
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