Non-uniform sampling, image recovery from sparse data and the discrete sampling theorem

Details Non-uniform sampling, image recovery from sparse data and the discrete sampling theorem Non-uniform sampling, image recovery from sparse data and the discrete sampling theorem

2008-08-27

arxiv.org/abs/0808.3728v1

Physics

Optics

Scientific paper

10.1364/JOSAA.26.000566

In many applications sampled data are collected in irregular fashion or are partly lost or unavailable. In these cases it is required to convert irregularly sampled signals to regularly sampled ones or to restore missing data. In this paper, we address this problem in a framework of a discrete sampling theorem for band-limited discrete signals that have a limited number of non-zero transform coefficients in a certain transform domain. Conditions for the image unique recovery, from sparse samples, are formulated and then analyzed for various transforms. Applications are demonstrated on examples of image super-resolution and image reconstruction from sparse projections.

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