**ABSTRACT**
### 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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