A multidimensional irregular sampling algorithm and applications

Author

Benedetto, John J. ; Wu, Hui-Chuan

Author_Institution

Dept. of Math., Maryland Univ., College Park, MD, USA

Volume

4

fYear

1999

fDate

15-19 Mar 1999

Firstpage

2039

Abstract

For a given spiral, a bandwidth B can be chosen and a sequence S can be constructed on the spiral with the property that all finite energy signals having bandwidth B can be reconstructed from sampled values on S. The bandwidth can be expanded as desired, and reconstruction is attained by constructing sampling sets on interleaving spirals. This solves a problem in MRI; and the algorithm can be modified to deal with irregular sampling problems in SAR. The algorithm is a consequence of our theoretical results, which in turn were inspired by seminal work on balayage in the 1960s by Beurling (1966) and Landau (1967). Our results depend on d-dimensional Fourier frames and tiling properties of spectral synthesis sets

Keywords

magnetic resonance imaging; multidimensional signal processing; radar signal processing; sequences; set theory; signal reconstruction; signal sampling; signal synthesis; spectral analysis; synthetic aperture radar; Fourier frames; MRI; SAR; bandwidth; finite energy signals; interleaving spirals; multidimensional irregular sampling algorithm; sampling sets; sequence; signal reconstruction; spectral synthesis sets; tiling properties; Bandwidth; Educational institutions; Image reconstruction; Interleaved codes; Magnetic resonance imaging; Mathematics; Multidimensional systems; Sampling methods; Signal synthesis; Spirals;

fLanguage

English

Publisher

ieee

Conference_Titel

Acoustics, Speech, and Signal Processing, 1999. Proceedings., 1999 IEEE International Conference on

Conference_Location

Phoenix, AZ

ISSN

1520-6149

Print_ISBN

0-7803-5041-3

Type

conf

DOI

10.1109/ICASSP.1999.758330

Filename

758330