A Kaczmarz-based approach to nonperiodic sampling on unions of rectangular lattices

Hans G. Feichtinger and Thomas Strohmer

We consider the reconstruction of a band-limited signal from a nonuniform sampling set having a special geometry. The sampling set consists of two or more uniform sampling lattices with possibly different sampling rate (each sampling rate being below Nyquist rate). We propose a block-Kaczmarz based method for signal reconstruction. The blocks are of Toeplitz type, their inverses can be calculated inexpensively applying fast Toeplitz solvers. Moreover computing the inverses in the Gohberg-Semencul form enables both economical storage and fast matrix-vector multiplications via FFT's. These facts allows to apply the proposed method to large-scaled real data problems. Furthermore the approach can easily be generalized to higher dimensions. We also focus on the behavior of the ACT method. Numerical experiments and comparisons to standard methods complete this note.

Keywords: algorithms, irregular sampling, numerical work

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