Title :
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
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;
Conference_Titel :
Acoustics, Speech, and Signal Processing, 1999. Proceedings., 1999 IEEE International Conference on
Conference_Location :
Phoenix, AZ
Print_ISBN :
0-7803-5041-3
DOI :
10.1109/ICASSP.1999.758330
