Nonuniform sampling, image recovery from sparse data and the discrete sampling theorem

In many applications, sampled data are collected in irregular fashion or are partly lost or unavailable. In these cases, it is necessary to convert irregularly sampled signals to regularly sampled ones or to restore missing data. We address this problem in the framework of a discrete sampling theorem for band-limited discrete signals that have a limited number of nonzero 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 superresolution and image reconstruction from sparse projections. (C) 2009 Optical Society of America