Electricity: measuring and testing – Particle precession resonance – Using a nuclear resonance spectrometer system
Patent
1997-01-10
2000-12-05
Oda, Christine K.
Electricity: measuring and testing
Particle precession resonance
Using a nuclear resonance spectrometer system
324314, G01R 3320, G01V 300
Patent
active
061571911
DESCRIPTION:
BRIEF SUMMARY
FIELD OF THE INVENTION
The invention is directed to a method for image acquisition from measured data of a nuclear magnetic resonance experiment that are entered into a measured data matrix with discrete k-space points, whereby a image matrix with image data is acquired from the measured data matrix by Fourier transformation, and whereby an image is displayed on the basis of the image data matrix.
DESCRIPTION OF THE PRIOR ART
A method of the above general type is disclosed, for example, in U.S. Pat. No. 5,168,226.
In traditional methods, the Fourier transformation required for image production is implemented according to what is referred to as an FFT (Fast Fourier Transform) algorithm, as described, for example, by Alfred v. Aho et al. in "The Design and Analysis of Computer Algorithms", Addison-Wesley Publishing Company, pages 257 through 264. This algorithm is very efficient since it requires only a fraction of the calculating operations compared to discrete Fourier transformation, however, it can only be applied when the length of the dataset to which the algorithm is to be applied represents a power of a whole number. The FFT method is usually applied to datasets having a length of 2.sup.n.
The limitation to specific dataset lengths, however, is undesirable for certain applications. For three-dimensional datasets, for example, the resolution within a slice should thus be capable of being arbitrarily set. This can in fact be achieved without further difficulty with a discrete Fourier transformation, however, the number of required calculating operations and thus the required calculating time, increases drastically. For example, given a dataset length of 512 more than one hundred times as many calculating operations are required for the discrete Fourier transformation than given the FFT algorithm.
Chirp-z transformation as disclosed in European Application 0 453 102 in its application to MR imaging is a method for image calculation that is independent of the dataset length. This method is noticeably faster than discrete Fourier transformation.
Utilizing a "Chirp-Z transformation" for the realization of a discrete Fourier transformation is known for certain applications such as, for example, "charge coupled devices" from the reference "Henry Nussbaumer, Fast Fourier Transform and Convolution Algorithms", Springer-Verlag, 1982, pages 112-115.
The technique of "Chirp-z Transformation" is explained in general for digital signal processing in the book, "Digitale Signalverarbeitung", Vol. I, H. W. Schussler, Springer Verlag 1988, pp. 70-72.
The reference, "IEEE Transactions on Medical Imaging", Vol. 9, No. 2, Jun. 2, 1990, pp. 190-201, describes the application of a chirp-z transformation for chemical shift imaging with magnetic resonance apparatus. This transformation is thereby utilized as substitute for the Fourier transformation for acquiring the spectrum, and an improved, spectral resolution is thus achieved. The Fourier transformation is utilized for the topical resolution, as usual.
The reference "Electrical Design News", Vol. 34, 1989, pages 161-170 describes the application of chirp-z transformation to the calculation of frequency spectra.
SUMMARY OF THE INVENTION
An object of the present invention is to implement a method for image reconstruction in a nuclear magnetic resonance tomography apparatus such that measured data matrices of an arbitrary size can be processed given low calculating time.
The above object is achieved in accordance with the principles of the present invention in a method for image acquisition from nuclear magnetic resonance measured data (x.sub.j,k) which are entered into a measured data matrix with discrete k-space points (j,k), with a Fourier transformation being implemented in a first direction for all k=0 . . . N-1 (wherein N is the number of rows in the matrix) and wherein the measured signals (x.sub.j,k) are acquired with an RF-phase modulation of the nuclear magnetic resonance signals according to a chirp function w.sup.k.spsp.2.sup./2, wherein the resulting data
REFERENCES:
patent: 5168226 (1992-12-01), Hinks
"Hi-Resolution NMR Chemical-Shift Imaging with Reconstruction by the Chirp z-Transform," Ma et al., IEEE Trans. on Med. Imaging, vol. 9, No. 2, Jun., 1990, pp. 190-201.
"Vergleichende Bewertung der Chirp-Z-Transformation (CZT) und der Fast-Fourier Transformation (FFT)," Pfeiffer et al., Elektrie, vol. 47, No. 10 (1993), pp. 370-374.
Chirp-Z Transform Efficiently Computed Frequency Spectra, Lyons, EDN-Electrical Design News, vol. 34, No. 11 (1989) pp. 161-170.
"Segmented Chirp Z-transform and Its Applications," Wang, Proceedings of ICASSP 89, IEEE Press, vol. 2, May 23-26, 1989, pp. 1003-1006.
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"The Design and Analysis of Computer Algorithms," Aho et al., Addison-Wesley Publishing Co., pp. 257-264.
"Fast Fourier Transform and Convolution Algorithms," 2.sup.nd Ed., Nussbaumer (Springer-Verlag 1982) pp. 112-115.
"Digitale Signalverarbeitung," Schussler, Springer-Verlag (1988), pp. 70-72.
Rabiner, L.R. schafer, R.W., Rader, C.M., The Chirp z-transformation and its applications; Bell System Technical Journal, 48, 1249-1292, 1969.
Rabiner, L.R. schafer, R.W. Rader, C.M., The Chirp z-transorm algorithm, IEEE Transactions Of Audion and Electroacoustics, vol. AU-17, Jun. 1969, pp. 86-92.
Oppenheim A.V. and R. W. Schaffer, Digital Signal Processing, Prentice-Hall, 1975, pp. 321-326.
Gaskill Jack D., Linear Systems, Fourier Transforms and Optics, John Wiley & Sons New York 1978 Chapter 6 pp. 150-157 and Chapter 7 pp. 196-200.
Merriam Webster's Collegiate Dictionary Tenth Edition 1997 Biographical Names section p. 1411.
Fetzner Tiffany A.
Oda Christine K.
Siemens Aktiengesellschaft
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