X-ray or gamma ray systems or devices – Specific application – Computerized tomography
Reexamination Certificate
1998-11-25
2001-01-09
Bruce, David V. (Department: 2876)
X-ray or gamma ray systems or devices
Specific application
Computerized tomography
C378S015000, C378S901000
Reexamination Certificate
active
06173030
ABSTRACT:
BACKGROUND OF THE INVENTION
This invention relates to X-ray imaging techniques, and, more particularly, to computerized tomography X-ray imaging using a minimal set of cone beam data measurements.
Computerized tomography (CT) uses a source of imaging energy such as X-ray energy and a detector for detecting imaging energy that has passed through an object of interest, often a patient being imaged for medical purposes. Typically, a single point source is used with an area detector such as an X-ray detector array.
Relative movement between the source, object of interest, and detector is used to collect data for image reconstruction purposes. Usually the source is moved, while the object and detector remain stationary relative to each other.
Typical source trajectories are “1 dimensional manifolds” described by parametric equations of a single variable. The advent of area X-ray detectors permits measurement of a 2 dimensional data set for each source position, since the detector lies in a 2 dimensional plane. Therefore, it is possible to measure a 1+2=3 dimensional data set of line integrals of the object being imaged.
This dimension count is encouraging for volummetric imaging such as CT because the imaged object lies in three spatial dimensions. More specifically, complete CT data for a family of parallel planes constitutes a 2+1=3 dimensional data set and completely determines the imaged object.
Unfortunately, cone beam data generated by a single point source does not permit simple reconstruction. A single circular trajectory does not provide a complete data set for Radon reconstruction (i.e., apart from measurement and discretization errors). Therefore, various scan trajectories have been used.
Among scan trajectories are two offset circular scans with a line extending between them.
Generally, the scan trajectories result from relative movement among the source, detector, and object being imaged. Usually, the source is moved in a path about the object to define the scan trajectory. The object being imaged is often a medical patient, but could also be an industrial part being imaged to locate possible defects. When the object being imaged is an industrial part, the scan trajectory may be defined at least partly by movement of the object relative to the source or relative to the detector. A scan trajectory might also be defined at least partly by movement of the detector.
Such scan trajectories that provide complete cone beam data may present a number of problems. The path or paths followed by the source or other component being moved may be complex. This requires a complex robotic function. Additionally, the scan time for obtaining a complete data set may be longer than desirable. Especially in the case where the imaged object is a patient, it is desirable to limit the time and dose of X-ray exposure. A complex scan path requires a longer time of exposure than a simple path. Yet, if the dose is reduced to partially compensate for a long exposure time, the signal to noise ratio is reduced. Errors in the data, particularly due to lag and signal to noise degradation with decreasing dose, often are more troublesome with complex scan paths. Further, a complex scan path increases the amount of measured data and this increase in data in turn increases computational demands when using the reconstruction process to provide an image.
Although it is possible to provide image reconstruction with a incomplete data set, such a reconstructed image will be quite inexact, if not undetermined, in some regions as a result of not having the missing data.
BRIEF SUMMARY OF THE INVENTION
In an exemplary embodiment of the method of the invention, an object is imaged by applying imaging energy from a source to the object. Imaging energy that has passed through the object is detected by a detector. The object is scanned with the imaging energy such that the detector collects measured image data of a “characteristic surface” corresponding to a “characteristic problem.” “Characteristic surface,” “characteristic problem” and the related “characteristic cone” are known mathematic concepts, but will also be defined in detail below. The characteristic problem is solved and the solution to the characteristic problem allows determination of a portion of the missing cone beam data. An image of the object is based on the measured image data and the determined missing cone beam data.
An exemplary embodiment of the system of the invention includes a source for applying imaging energy to the object. A detector detects imaging energy that has passed through the object. A positioner scans the object with the imaging energy such that the detector collects measured image data over a characteristic surface corresponding to a characteristic problem. An extrapolator extrapolates to solve the characteristic problem and determine missing cone beam data. An image supplier supplies an image of the object based on the measured image data and the determined missing cone beam data.
REFERENCES:
patent: 5465283 (1995-11-01), Tam
patent: 6009142 (1999-12-01), Sauer et al.
Fritz John, “The Ultrahyperbolic Equation with 4 Independent Variables”, Duke Math. Journal, pp. 300-322 (1938).
Leifur Asgeirsson, “Uber eine Mittelweretseigenschaft von Loesungen homogeneer linearer partieller Differentialgleichungen 2. Ordnung mit konstanten Koeffizienten”, Mathematische Annalen, 13, pp. 321-346 (1938) with Englinsh language translation.
Glynn Owens, “An Explicit Formula for the Solution of the Ultrahyperbolic Equation in Four Variables”, Duke Math Hournal, 9, pp. 272-282 (1942).
Glynn Owens “A Boundary-Value Problem for Analytic Solutions of an Ultrahyperbolic Equation”, Duke Math Hournal, 20, pp. 29-38 (1953).
Copending U.S. Patent application Serial No. 09/113,841, filed Jul. 10, 1998, by S. Patch, entitled “Almost-Everywhere Extrapolation from Cone-Beam Data”.
Bruce David V.
General Electric Company
Ingraham Donald S.
Stoner Douglas E.
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