New variants of the POCS method using affine subspaces of finite codimension, with applications to irregular sampling

C.Cenker, H.G. Feichtinger, M.Mayer, H.Steier, and T.Strohmer

The POCS-method (projection onto convex subsets) has been proposed (see Yeh/Stark) as an efficient way of recovering a band-limited signal from irregular sampling values. However, both the ordinary POCS-method (which uses one sampling point at a given time, i.e. consists of a succession of projections onto affine hyper-planes) and the one-step method (which uses all sampling values at the same time) become extremely slow if the number of sampling points gets large. Already for mid-size 2D-problems (e.g. 128*128 images) one may easy run into memory problems. Based on the theory of pseudo-inverse matrices new efficient variants of the POCS-method (so to say intermediate versions) are described, which make use of a finite number of sampling points at each step. Depending on the computational environment appropriate strategies of designing those families of sampling points (either many families with few points, or few families with many points, overlapping families or disjoint ones...) have to be found. We also report on numerical results for these algorithms.

Keywords: algorithms, irregular sampling, numerical work

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