Natural k-plane coordinate reconstruction method for magnetic resonance imaging: Mathematical foundations
✍ Scribed by Gordon E. Sarty
- Publisher
- John Wiley and Sons
- Year
- 1997
- Tongue
- English
- Weight
- 237 KB
- Volume
- 8
- Category
- Article
- ISSN
- 0899-9457
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✦ Synopsis
The mathematical basis and motivation for a new, noninbe more natural, literally, to use gradient fields that varied continterpolative, direct method for reconstructing magnetic resonance imuously instead of being switched. The method of spiral imaging aging (MRI) data is presented. The reconstruction method is called uses continuously varying gradient fields, and other k-space patthe natural k-plane coordinate reconstruction method (NKPCRM) and terns are possible. Therefore, another motivation for constructing can be used for reconstructing MRI data collected in the presence the NKPCRM was to obtain a generic reconstruction method that of continuously varying gradient magnetic fields. A continuous, theocould be applied directly to any MRI k-space scan pattern. The retically useful NKPCRM is presented along with a practical discrete idea was that the k-space pattern should be chosen to minimize NKPCRM both for single-and multiple-shot data acquisitions. The the acquisition time and hardware requirements without considercontinuous method gives rise to continuous operators on function ation of reconstruction time. With dependence on the FFT respaces that can be characterized as integrable curve band-pass operators. The discrete reconstruction method reduces to a Fourier sum-moved, we approach the problem from scratch. Reconstruction mation weighted by the Jacobian of a ''naturally'' chosen coordinate time is important, but it is viewed as a separate problem to be system. In the case of a Cartesian coordinate system, the new method solved after a generic reconstruction method is derived and mathreduces to the discrete Fourier transform normally used for MRI reematically examined.
construction. The NKPCRM is rigorously analyzed from a mathemati-
The article is organized as follows. In Section II, a brief decal point of view, and specific implementations such as Lissajous, scription of the signal model and mathematical framework of the spiral, and rose scans are discussed. ᭧