Generalized reconstruction technique

Details Generalized reconstruction technique Generalized reconstruction technique

1985-08-09

1987-10-20

Tokar, Michael J.

Electricity: measuring and testing

Particle precession resonance

Using a nuclear resonance spectrometer system

324307, G01R 3320

Patent

active

047017066

ABSTRACT:
The resonance signals from a magnetic resonance imaging apparatus are discretely sampled. The sampled data are non-uniform in data space due to motion, eddy currents in the magnetic field, inaccurate timing in the application of the gradient magnetic fields, non-uniform sampling of the data, or the like. The discretely sampled data, s(k.sub.x, k.sub.y), is mapped from data space to image space by a generalized transform. The generalized transform, unlike a Fourier transform, concurrently corrects for the non-uniformity as it transforms the non-uniform data space data into image space data with a preselected distribution, e.g. uniform. For a given y position of non-uniformly sampled data s(k,y), the estimated spin density .rho.(x,y) is related to the actual spin density .rho.(x,y) by the equation: ##EQU1## where the matrix A describes the non-uniformity and can be calculated or determined experimentally. When the matrix B=A.sup.-1, the estimated and actual data match. In one embodiment, the generalized transform algorithm is determined by inverting the matrix A and operating on a data matrix therewith.

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The Fourier Transform and Its Applications pp. 200-201.

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