Electricity: measuring and testing – Particle precession resonance – Using a nuclear resonance spectrometer system
Reexamination Certificate
2001-03-21
2003-04-08
Lefkowitz, Edward (Department: 2862)
Electricity: measuring and testing
Particle precession resonance
Using a nuclear resonance spectrometer system
C324S309000
Reexamination Certificate
active
06545472
ABSTRACT:
BACKGROUND OF THE INVENTION
1. Field of the Invention
The invention relates to a magnetic resonance imaging method for forming a magnetic resonance image, wherein magnetic resonance signals are acquired by receiving antennas via a plurality of signal channels, which individual receiving antennas have respective sensitivity profiles. The invention also relates to a magnetic resonance system.
2. Description of the Related Art
A magnetic resonance imaging method and a magnetic resonance system for carrying out such a magnetic resonance imaging method are known from the article “Coil Sensitivity Encoding for Fast MRI” by K.P. Prüssmann et al. in Proceedings ISMRM (1998), 579.
The known magnetic resonance imaging method is known by the acronym SENSE method. This known magnetic resonance imaging method utilizes receiving antennas in the form of receiving coils. This magnetic resonance imaging method utilizes sub-sampling of the acquired magnetic resonance signals so as to reduce the time required to scan the k-space at a sampling density in the k-space for the desired field-of-view and over a region in k-space which is large enough for the desired spatial resolution of the magnetic resonance image. Notably the respective lines in the k-space along which scanning is performed are situated apart further in the k-space than is necessary for the desired spatial resolution. In other words, “lines are skipped” in the k-space. As a result of such “skipping of lines in the k-space”, less time is required for the acquisition of the magnetic resonance signals. Receiving coil images are reconstructed on the basis of the sub-sampled magnetic resonance signals from the individual receiving coils. Due to the sub-sampling, the actual field of view is reduced so that back-folding or aliasing artefacts occur in such receiving coil images. The magnetic resonance image is derived from the receiving coil images on the basis of the sensitivity profiles, the aliasing artefacts in the magnetic resonance image thus being substantially or even completely removed. This unaliasing operation enlarges the magnetic resonance image to the desired field of view.
It has been found in radiological practice the time required for the acquisition of the magnetic resonance signals need still be reduced considerably further. It has been found that a substantial reduction of the acquisition time of the magnetic resonance signals is necessary notably for magnetic resonance imaging methods for the imaging with a high spatial resolution of fast moving parts of the anatomy, for example the beating heart of a patient under stress, but also for MR angiography.
SUMMARY OF THE INVENTION
It is an object of the invention to provide a magnetic resonance imaging method wherein the acquisition time of the magnetic resonance signals is significantly shorter than the acquisition time required when the known SENSE technique is used.
This object is achieved by the magnetic resonance imaging method according to the invention wherein the noise correlation between individual signal channels is represented by a noise correlation matrix, where the magnetic resonance signals are acquired with sub-sampling, regularly resampled magnetic resonance signals are resampled on a regular sampling grid from the acquired magnetic resonance signals, the noise correlation matrix is approximated by a block diagonal matrix or a band diagonal matrix, the matrix elements situated outside a predetermined band around the main diagonal of the approximated noise correlation matrix have the value zero, and the magnetic resonance image is reconstructed from the regularly resampled magnetic resonance signals which have been resampled from acquired magnetic resonance signals on the basis of the sensitivity profiles and the approximated noise correlation matrix.
The magnetic resonance image is derived from the magnetic resonance signals sub-sampled in the k-space while utilizing the sensitivity profiles. Sub-sampling means that the sampling in the k-space is coarser, i.e. with a resolution in the k-space which is coarser than sufficient for the field of view of the magnetic resonance image. In a magnetic resonance imaging method the smallest wavelength of brightness variations in the magnetic resonance image relates to the field of view. The smallest wavelength is notably proportional to the magnitude of the field of view and to the sampling density in the k space. In the case of sub-sampling the sampling is coarser than sufficient for the desired size of the field-of-view of the magnetic resonance image. The signal values are encoded on the basis of their wave vectors in the k-space and on the basis of the sensitivity profiles. The magnetic resonance signals of the respective receiving antennas correspond to respective signal channels. The noise contribution to the signals in each of the signal channels is a linear combination of noise contributions from the relevant signal channel and from (in principle) all other signal channels. The receiving antennae are, for example receiving coils that are sensitive to the magnetic resonance signals. Preferably, surface coils are used as the receiving antennas. Such surface coils are arranged on the body of the patient to be examined and pick up notably magnetic resonance signals which are generated in the body of the patient to be examined in positions situated near the surface coil. The noise correlation between the signal channels is represented by a noise correlation matrix. For realistic numbers of magnetic resonance signals for a magnetic resonance image of diagnostic quality, the decoding of the magnetic resonance signals in the k-space and on the basis of the sensitivity profiles into pixel values for individual pixel positions in an image matrix constitutes,if no steps are taken, a matrix inversion problem requiring a high calculation capacity and long calculation times.
The noise correlation matter may be approximated by the unity matrix, a block diagonal matrix or a two diagonal matrix, which are all special examples of block diagonal or band diagonal matrices. Reconstruction of the magnetic resonance image from the sub-sampled magnetic resonance signals on the basis of the SENSE-algorithm includes optimisation of noise properties in the magnetic resonance image. This optimisation involves a noise correlation matrix which contains in the the diagonal elements noise in the sampled magnetic resonance signals and in the off-diagonal elements noise correlations between respective sampled magnetic resonance signals acquired by different receiver antennae. It appears that as an approximation the noise correlation matrix may be replaced by the unity matrix. An alternative, more subtle, approximation is based on the recognition that the noise correlations are about constant over time. Hence, it appears that the noise correlation can adequately be described by a matrix having a sparse structure, i.e. approximately (block) diagonal. This sparse sructure allows a virtual re-sampling or re-binning of the sub-sampled magnetic resonance signals from the respective receiver coils into virtual channels as linear combinations of the sub-sampled magnetic resonance signals from the individual receiver coils. The weights involved in this linear combination are obtained from the so-called Cholesky decomposition of the noise correlation matrix into a matrix product of an invertible left triangular matrix and its Hermitian conjugate. Then, the effective noise correlation matrix connecting the virtual channels is the unit matrix. It has been found according to the invention that in practice the correlation between noise contributions in the magnetic resonance signals from individual receiving antennas can be suitably approximated by a simpler matrix with contributions from only the vicinity of the main diagonal. It has even been found that this noise correlation may be replaced by the unity matrix. It has even been found that such a simplification strongly mitigates the matrix inversion problem, so that only a comparatively short calculation
Börnert Peter
Prüssmann Klaas Paul
Weiger Markus
Fetzner Tiffany A.
Koninklijke Philips Electronics , N.V.
Lefkowitz Edward
Vodopia John
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