X-ray or gamma ray systems or devices – Specific application – Computerized tomography
Patent
1999-01-25
2000-11-21
Bruce, David V.
X-ray or gamma ray systems or devices
Specific application
Computerized tomography
378901, A61B 603
Patent
active
061513776
DESCRIPTION:
BRIEF SUMMARY
INTRODUCTION
The present invention regards computer tomography and methods of evaluating tomography data. The method of the invention can be applied to all kinds of tomographic imaging, whether registered by X-ray or radioactive absorption, by magnetic resonance (MR) or positron emission tomography (PET). In all those cases are obtained experimental values in the form of line integrals along multitudes of straight lines. The typical CT measurement consists of mounting an X-ray tibe on a rotatable circular ring and set of detectors in a row opposite the tube.
The invention therefore regards a computer tomography method of the kind recited in the preamble of claim 1.
In computerized tomographic imaging (CT) the inverse problem consists of determining a function from its line integrals. We examine three different types of measured data sets, with different scanning geometries, namely two versions of parallel scanning (sinogram, linogram) and fan-beam scanning (even cone-beam scanning). We will study the Filtered Backprojection Method (FBM) which is one of the most well-known and widely used methods. The reason for the widh use of the filtered backprojection algorithm is the high image quality.
A serious problem in prior art evaluation of tomographic data in order to obtain an image is the heavy computational complexity for the back-projection operator, which is of the order N.sup.3. It is the general object of the invention to obtain an improved method of transforming tomographic data into images, which is less complex and can give improvement either in computational speed or in an increased number of voxels/pixels in an image.
This object and other objects and advantages are obtained, according to the invention, by means of a computer tomography method of the kind recited, which is characterized by the steps recited in claim 1. Advantageous embodiments are recited in dependent claims.
In conventional backprojection each pixel value is calculated separately, which means that O(N) operations are required for each pixel. Then the total number of operations will be of the order O(N.sup.3). Instead of directly doing the N.sup.3 additions the basic idea behind the new algorithm is to divide the summation into partial sums, which then are used to form new partial sums in a dyadic and hierarchial way, see FIG. 1. The reason for this procedure is the benefit in computational reduction due to the fact that a partial sum has approximately the same value for many neighbouring points. Thus each value of a partial sum is calculated once, but used several times when forming a new partial sum from two partial sums in a preceding level of the hierarchy.
Although in the present description, the invention is exemplified with forming hierachial partial sums in a dyadic way, which is presently believed to be the best mode, it is also possible to sum more than two groups, namely, each time a number which is a prime number. It is even not necessary to use the same prime number in each stage.
In a preferred embodiment, families of lines are combined two and two, indicating that the total number of line families is a power of two. With a number of pixels/voxels of 512.times.512 an an equal number of families, i.e. angles of registration, this condition is fulfilled. However, without using the full advantages of the invention, it is possible in the partial sum calculation to combine three (or five, or any prime number) space distributions by making sums for those points where the lines for the largest angular difference intersect, and adding interpolation values for the further distributions.
It is also possible to add line integrals for intermediate lines, for which no measurement was made, i.e. by setting intermediate (non-measured) line integrals to the mean value of the adjacent lines, for which a measurement was made.
Although the method is most easily understood for a case where all the line families belong to the same plane, which is the most common configuration in practice, and which is exemplified as the fan-type, the sino
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