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.

No abstract

Color videos acquired with a single CCD through turbulent media can be enhanced in their resolution beyond the limit defined by the image sampling rate. We provide a mathematical justification for this claim, present an efficient superresolution algorithm and its experimental verification on a real-life video, and finally, discuss its potentials and limitations.

Signal decomposition with an overcomplete dictionary is nonunique. Computation of the best approximation is known to be NP-hard problem. The matching pursuit (MP) algorithm is a popular iterative greedy algorithm that finds a sub-optimal approximation, by picking at each iteration the vector that best correlates with the present residual. Choosing approximation vectors by optimizing a correlation inner product can produce a loss of time and frequency resolution. We propose a modified MP, based on a post processing step applied on the resulting MP approximation, using backward greedy algorithm, to achieve higher resolution than the original MP.

No abstract