**ABSTRACT**
### Recovery of missing segments and lines in images

#### H.G. Feichtinger and T.Strohmer

The so-called irregular sampling problem is concerned with the problem of
reconstruction of an image from irregularly located samples. In a series of
papers (many of them together with K. Gröchenig) the authors have
developed
new algorithms for efficient reconstruction of signals from arbitrary
sampling
sets, which are guaranteed to converge as long as the image is band-limited
and the sampling set does not have too big holes. It is however
experimental
evidence that for a typical real world image very satisfactory
reconstructions
can be obtained even if it is not band-limited in the strict sense.

In the present paper only a certain type of irregularities is considered,
i.e. missing lines or missing rectangles in a given image. This problem
occurs in practical situations where such parts may be lost during the
transmission of an image or badly recorded by a camera. The basic idea is
to
solve the problem by iterative solution of one-dimensional subproblems,
i.e. by interpolation along horizontal and then vertical lines or vice
versa. The use of fast and efficient 1-D reconstruction methods is the
basis
for very fast and highly parallelizable algorithm. We demonstrate the
efficiency of the product ACT algorithm by typical applications.

**Keywords:** algorithms, irregular sampling, numerical work

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