Local reconstruction of a function from a non-uniform sampled data. (English) Zbl 1180.65183
The article is devoted to digital data processing. In the case of the data sample set is uniform the answer is given by the Shannon’s sampling theorem. In the communication theory – for satellite pictures, biomedical images, for the missing data problem – a non-uniform sample set plays a crucial role. The authors present a method of solving the non-uniform data problem for signals of a moderate decay in the frequency domain.
Reviewer: Vladimir N. Karpushkin (Moskva)
MSC:
| 65T40 | Numerical methods for trigonometric approximation and interpolation |
| 42C15 | General harmonic expansions, frames |
| 42C40 | Nontrigonometric harmonic analysis involving wavelets and other special systems |
| 94A20 | Sampling theory in information and communication theory |
| 65T60 | Numerical methods for wavelets |
Keywords:
non-uniform sampling; Hermite function; scaling identity; shift invariant space; wavelet; digital data processingReferences:
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