Image reconstruction

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25036303, 378901, A61B 603

Patent

active

056419651

DESCRIPTION:

BRIEF SUMMARY
This invention relates to the reconstruction of images, particularly tomographic images representing the distribution of some characteristic across a sectional plane of a body under investigation, from measurements made peripherally of the sectional plane.
The invention relates particularly, but not exclusively, to the SPECT (single photon emission computed tomography) and PET (positron emission tomography) tomographic techniques and to that known variously as electrical impedance tomography or applied potential tomography and referred to hereinafter as EIT, in which electrical signals applied peripherally to points of a body under investigation result, at other peripheral points, in electrical voltages or currents of which the values are measured and processed to form an image representing the distribution of electrical conductivity or resistivity over a section of the body. Such techniques have been described in, for example, a paper entitled "Applied potential tomography" by D. C. Barber and B. H. Brown published in J.Phys. E: Sci.Instrum., Vol. 17 (1984), pages 723-33, and in other papers referred to therein or published subsequently.
EIT has a promising future in clinical investigation of the human body, because it is a relatively inexpensive tomographic technique in terms of the equipment required, is essentially non-invasive, enables data to be rapidly collected and processed, and can be used for continuous monitoring.
In clinical use of the EIT technique, typically, a ring of spaced electrodes, say 16 in number, are positioned round and in contact with a body segment such as the thorax and an alternating current driving signal of a few milliamps at a frequency of, say, 50 kHz is applied between two of the electrodes while the resulting currents or voltages between remaining pairs of electrodes are measured and their values stored for processing. The driving signal is applied successively to different pairs of electrodes, and at each step the signals at the remaining pairs of electrodes are measured and their values stored, so as to maximise the amount of independent data which is obtained and which is then processed to obtain maximum resolution of the reconstructed image. The number of electrodes employed imposes an upper limit on the amount of independent data which can be obtained, and to increase the amount of data available, and thus the image resolution obtainable, it is necessary to increase the number of electrodes employed. There remains, however, a further problem: reconstruction of an image from the measured data is essentially a problem of matrix algebra, and, as the amount of data to be processed increases, the difficulty involved in applying the currently-employed reconstruction algorithms increases disproportionately. This problem is encountered not only in connection with EIT but also with other computed tomographic techniques, such as SPECT and PET, which employ back-projection from measured data to derive a reconstructed image.
Accordingly, it is an object of the present invention to provide an improved reconstruction method or algorithm for deriving a reconstructed tomographic image from the relevant basic measured data, and an improved method of formulating a critical part of such algorithm.
According to the invention there is provided a back-projection image reconstruction method or algorithm of the type B(FB).sup.-1 g=c, where c is the image data vector which is to be reconstructed, g is, arranged in suitable form, the measurement data vector from which the image data vector c is to be reconstructed, F is a matrix representing the forward operation from c to g and B is a matrix representing the corresponding direct back-projection operation, characterised in that for the matrix (FB).sup.-1 there is substituted the equivalent, computationally more amenable, matrix product WQ.sup.-1 W* wherein W* is the complex conjugate of W, Q.sup.-1 is the inverse of a matrix Q obtainable from the matrix FB by the operation Q=W*(FB)W and W is a matrix related to the Fourier Transform and defin

REFERENCES:
patent: 5079697 (1992-01-01), Chesler
patent: 5490516 (1996-02-01), Hutson
Llacer & Meng: "Matrix-based image reconstruction methods for tomography", IEEE Transaction on Nuclear Science, vol. NS-32, No. 1, Feb. 1985, pp. 855-864.

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