ISSN:
1572-9036
Keywords:
distributional harmonic analysis on the Heisenberg group G
;
Kepplerian temporospatial phase triangulation procedure
;
geometric quantization
;
planar coadjoint orbit stratification of G
;
calculus of Schwartz kernels
;
transvectants
;
symplectically invariant symbol calculus of pseudodifferential operators
;
symplectic filter bank processing
;
quantum holography
;
symplectic Fourier transform inversion
;
infinitesimal generator of smooth dynamical systems
;
Fourier transform magnetic resonance imaging
;
Lauterbur spatial encoding technique
;
clinical neurodiagnostic imaging
;
noninvasive radiodiagnostics
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract Due to its unequalled advantages, the magnetic resonance imaging (MRI) modality has truly revolutionized the diagnosis and evaluation of pathology. Because many morphological anatomic details that may not be visualized by other high tech imaging methods can now be readily shown by diagnostic MRI, it has already become the standard modality by which all other clinical imaging techniques are measured. The unique quantum physical basis of the MRI modality combined with the imaging capabilities of current computer technology has made this imaging modality a target of interdisciplinary interest for clinicians, physicists, biologists, engineers, and mathematicians. Due to the fact that MRI scanners perform corticomorphic processing, this modality is by far more complex than all the other high tech clinical imaging techniques. The purpose of this paper is to outline a phase coherent wavelet approach to Fourier transform MRI. It is based on distributional harmonic analysis on the Heisenberg nilpotent Lie group G and the associated symplectically invariant symbol calculus of pseudodifferential operators. The contour and contrast resolution of MRI scans which is controlled by symplectic filter bank processing gives the noninvasive MRI modality superiority over X-ray computed tomography (CT) in soft tissue differentiation.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1005704725676
Permalink
