Electricity: measuring and testing – Particle precession resonance – Using a nuclear resonance spectrometer system
Reexamination Certificate
1999-03-19
2001-09-11
Oda, Christine (Department: 2862)
Electricity: measuring and testing
Particle precession resonance
Using a nuclear resonance spectrometer system
C324S309000
Reexamination Certificate
active
06288542
ABSTRACT:
BACKGROUND OF THE INVENTION
1. Field of the Invention
The invention relates to an imaging method for medical examinations which includes the following steps:
acquiring a set of measurement values at measuring points distributed in the frequency domain,
weighting the measurement values in dependence on the density of the measuring points,
generating an image in the space domain by applying a Fourier transformation to the weighted measurement values of the set.
2. Description of Related Art
ISMRM 1996, page 359, discloses a method of this kind for the field of MR examinations (MR=Magnetic Resonance). According to the known method, the weighted measurement values are first convoluted with a gridding kernel so as to enable a Fast Fourier Transformation (FFT) to be carried out. After the FFT, the resultant values must be divided by the Fourier transform of the gridding kernel so as to obtain a perfect image.
In the case of a method in which the measuring points are not equidistantly distributed in the frequency domain, it is necessary to weight the measurement values in dependence on the density of the measuring points (the lower the density, the higher the weight with which a measuring point is taken into account). In the case of such irregular distributions the customary definition of the density as a number of measuring points per space interval does not make sense, because this measure fluctuates as a function of the magnitude of the space interval and an infinitely small space interval cannot be suitably considered. According to the known method, the measuring points are situated on a spiral, or on a plurality of spiral arms, and the density for a measuring point is defined as the content of the surface area enclosed by the perpendicular bisectors to the connecting lines to the preceding and the next measuring points with neighbouring spiral arms. This method is not suitable for sequences of the EPI type or other MR sequences involving a very irregular distribution of the measuring points. During MR examinations such an irregular distribution may also occur due to eddy currents or non-ideal gradient amplifiers or due to the use of methods involving asymmetrical echos.
SUMMARY OF THE INVENTION
Therefore, it is an object of the invention to conceive a method of the kind set forth in such a manner that it operates perfectly, and hence produces high-quality images, also in the case of very irregular distributions of the measuring points. This object is achieved according to the invention in that the measurement values are weighted in conformity with the magnitude of the Voronoi cells enclosing the measuring points associated with the measurement values.
The invention is based on the recognition of the fact that the magnitude of the Voronoi cells enclosing the individual measuring points constitutes a substantially optimum measure of the density of the measuring points at the area of the relevant measuring point. Therefore, when the measurement values acquired at the various measuring points are weighted in conformity with the magnitude of the Voronoi cells, Fourier transformation of the measurement values thus weighted will yield an optimum image.
Voronoi cells are known inter alia from ACM Computing Surveys, Vol. 23, No. 3, September 1991, pp. 345 to 350, and are irregular polygons (in case the measuring points are distributed in a two-dimensional frequency domain) or polyhedrons (for the three-dimensional case). The boundaries of these Voronoi cells enclose all points in the frequency domain which are situated nearer to the relevant measuring point than any other measuring point.
The invention can be used not only for measuring points in the two-dimensional space, but also for measuring point distributions in the three-dimensional or more-dimensional space (for example, for three-dimensional imaging spectroscopy) yielding three-dimensional or more-dimensional images. Therefore, in this context the term “image” is to be interpreted in its broadest sense.
Moreover, the invention is not only suitable for MR examinations but also for X-ray computer tomography (CT). CT images are customarily derived from the measurement values by convolution, but this method fails when the measurement values are not uniformly distributed in space, for example due to mechanical instabilities. In this case a CT image, however, can be reconstructed by means of a Fourier transformation for which the measurement values must be weighted in dependence on their density.
The least amount of calculation work is required when the images are reconstructed from the measurement values by means of a fast Fourier transformation (FFT); however, this implies that the measurement values lie at the grid points of a cartesian grid. A method which includes applying a convolution kernel to the measurement values in order to determine interpolated values at the grid points of a cartesian grid, applying a fast Fourier transformation to the set of measurement values, subjected to the convolution, in order to generate an image, and compensating the convolution-induced modulation of the image values associated with the individual pixels of said image.
The Voronoi cells of measuring points situated at the edge of the frequency domain are not closed at the outside, because no further measurement points are present therebeyond. These measuring points (corresponding to the high-frequency components), therefore, would enter the reconstruction with an excessive weight if the boundary of the frequency space were used as the outer boundary of the Voronoi cells. Artefacts thus induced could be avoided by reconstructing the image exclusively by means of measurement values whose associated measuring points are situated within completely enclosed Voronoi cells, but a part of the measurement values would then be lost to the reconstruction. This can be avoided in the version of the method which includes defining synthetic sampling points which are situated outside the measuring range in the frequency domain and whose position in relation to the externally situated measuring points is determined from the position of these measuring points in relation to the measuring points neighbouring these points in the inwards direction, and deriving the outer boundary of the Voronoi cells enclosing the outer measuring points while taking into account the sampling points.
This invention also includes particular application of the methods described above to an MR examination method and to an MR system.
REFERENCES:
patent: 5850229 (1998-12-01), Edelsbrunner et al.
“A Survey of a Fundamental Geometric Data Structure” by Franz Aurenhammer in ACM Computing Surveys, vol. 23, No. 3, Sep. 1991, pp. 345-350.
Proksa Roland
Rasche Volker
Sinkus Ralph
Fetzner Tiffany A.
Oda Christine
U.S. Philips Corporation
Vodopia John F.
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