Practices of irregular sampling

Based on a frame theoretical formulation of irregular sampling, conditions on sampling points are derive. Our formulation and sampling conditions are applicable to all subspaces (e.g. shift invariant, Gabor, bandlimited and bandpass subspaces). A focus is paid to the implementation of the algorithm in general. The method starts from constructing a pair of frame for a selected subspace, with which a sequence of sampling functions is fabricated based on a set of given irregular sampling points. The (irregular) sampling reconstruction is implemented through a frame-based iterative algorithm, which is guaranteed to converge. A matlab package with a graphic user interface will be provided for users to view demos as well as try their own sampling reconstruction problem. Users are also allowed to construct their own subspaces. Parameters, sampling points and signals may all be entered by users. The program will automatically check for the fulfillment of the sampling conditions and provide a reconstruction of the signal. We believe that this is a useful tool for studies and practices of irregular samplings.