Method and apparatus for reconstruction of the attenuation density of an object from X-ray projection image data
First Claim
1. A method for reconstruction of the attenuation density of an object from X-ray projection image data values, comprising the steps of:
- representing the attenuation density of said object by a sum of predetermined continuous harmonics with unknown coefficients;
relating each of said X-ray projection image data values to an integral of the attenuation density of said object, and thus to a corresponding sum of sums of said predetermined continuous harmonics with unknown coefficients;
determining said unknown coefficients from the relations between each of said X-ray projection image data values and the respective corresponding sum of sums of said predetermined continuous harmonics with unknown coefficients; and
reconstructing the attenuation density of said object by said sum of predetermined continuous harmonics with said determined coefficients.
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Abstract
A method for reconstruction of object attenuation density (S(x,y,z)) from X-ray projection image data values (V(pq)) comprises the steps of: representing (11) the object attenuation density by a sum of predetermined continuous harmonics (Hijk(x,y,z)) with unknown coefficients (aijk); relating (12) each of the projection image data values to an integral (S(pq)) of the object attenuation density, and thus to a corresponding sum of sums (aijk*Hijk(pq)) of the predetermined continuous harmonics with unknown coefficients; determining (13) the unknown coefficients (aijk) from the above relation; and reconstructing (14) the object attenuation density by said sum of predetermined continuous harmonics with said determined coefficients. The spatial three-dimensional object attenuation density is found as a continuous function with uniform resolution over all its volume and is shown as a solid three-dimensional body, which can be cut in arbitrary way and shown in continuous motion.
6 Citations
18 Claims
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1. A method for reconstruction of the attenuation density of an object from X-ray projection image data values, comprising the steps of:
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representing the attenuation density of said object by a sum of predetermined continuous harmonics with unknown coefficients; relating each of said X-ray projection image data values to an integral of the attenuation density of said object, and thus to a corresponding sum of sums of said predetermined continuous harmonics with unknown coefficients; determining said unknown coefficients from the relations between each of said X-ray projection image data values and the respective corresponding sum of sums of said predetermined continuous harmonics with unknown coefficients; and reconstructing the attenuation density of said object by said sum of predetermined continuous harmonics with said determined coefficients. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15)
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13. A method for reconstruction of the attenuation density of an object from X-ray projection image data values, comprising the steps of:
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approximating the attenuation density S(x,y,z) of said object by predetermined continuous harmonics Hijk(x,y,z) with unknown coefficients aijk according to S(x,y,z)=Σ
aijk*Hijk(x,y,z), where the number of said harmonics is lower than the number of said X-ray projection image data values;relating each of said X-ray projection image data values V(pq) to the attenuation density of said object according to −
ln(V(pq)=S(Pq), q=1, 2, 3, . . . , where S(Pq) is a sum of attenuation density values of said object;relating each of said X-ray projection image data values V (Pq) tosaid harmonics according to −
ln(V(Pq))=Σ
aijk*Hijk(Pq) to form a linear equation system, where Hijk(Pq) is a sum of harmonics corresponding to said sum of attenuation density values of said object;calculating the unknown coefficients aijk by solving said linear equation system; and reconstructing the attenuation density of said object by calculating S(x, y, z)=Σ
aijk*Hi;
k (x, Y, z). - View Dependent Claims (14, 18)
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16. An apparatus for reconstruction of the attenuation density of an object from X-ray projection image data values, said apparatus comprising:
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means provided to represent the attenuation density of said object by a sum of predetermined continuous harmonics with unknown coefficients; means provided to relate each of said X-ray projection image data values to an integral of the attenuation density of said object, and thus to a corresponding sum of sums of said predetermined continuous harmonics with unknown coefficients; means provided to determine said unknown coefficients from the relations between each of said X-ray projection image data values and the respective corresponding sum of sums of said predetermined continuous harmonics with unknown coefficients; and means provided to reconstruct the attenuation density of said object by said sum of predetermined continuous harmonics with said determined coefficients. - View Dependent Claims (17)
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Specification