Nonuniform sampling and spiral MRI reconstruction

John J. Benedetto; Hui Chuan Wu

doi:10.1117/12.408588

4 December 2000 Nonuniform sampling and spiral MRI reconstruction

John J. Benedetto, Hui Chuan Wu

Proceedings Volume 4119, Wavelet Applications in Signal and Image Processing VIII; (2000) https://doi.org/10.1117/12.408588
Event: International Symposium on Optical Science and Technology, 2000, San Diego, CA, United States

Abstract

There is a natural formulation of the Classical Uniform Sampling Theorem in the setting of Euclidean space, and in the context of lattices, as sampling sets, and unit cells E, e.g., the Voronoi cell. For sampling at the Nyquist rate, the sampling function corresponds to the since function, and it is an integral over E. The set E is a tile for Euclidean space under translation by elements of the reciprocal lattice. We have a constructive, implementable non-uniform sampling theorem in the context of uniformly discrete sampling sets and sets E, corresponding to the unit cells of the uniform sampling result. The set E has the property that the translates by the sampling set of the polar set of E is a covering of Euclidean space. The theorem depends on the theory of frames, and can be viewed as a modest generalization of a theorem of Beurling. The application herein is to fast magnetic resonance imagine by direct signal reconstruction from spectral data on spirals.

Citation Download Citation

John J. Benedetto and Hui Chuan Wu "Nonuniform sampling and spiral MRI reconstruction", Proc. SPIE 4119, Wavelet Applications in Signal and Image Processing VIII, (4 December 2000); https://doi.org/10.1117/12.408588

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