Method and apparatus for reconstruction of the attenuation density of an object from x-ray projection image data

• US 20050152505A1
• Filed: 03/02/2004
• Published: 07/14/2005
• Est. Priority Date: 01/13/2004
• Status: Active Grant

• Current Assignee: Xcounter AB (Varex Imaging Corporation)
• Original Assignee: Xcounter AB (Varex Imaging Corporation)
• Inventors: Sokolov, Skiff
• Granted Patent: US 6,973,156 B2
• Time in Patent Office: Days
• US Class Current: 378/210
• CPC Class Codes: A61B 6/583 using calibration phantoms
• CPC Class Codes: G01N 23/04 and forming images of the material
• CPC Class Codes: G01N 23/044 using laminography or tomosynthesis
• CPC Class Codes: G06T 11/006 Inverse problem, transformation from projection-space into object-space, e.g. transform methods, back-projection, algebraic methods
• CPC Class Codes: G06T 2211/436 Limited angle
• CPC Class Codes: Y10S 378/901 Computer tomography program or processor

Abstract

A method for reconstruction of object attenuation density (S(x,y,z)) from X-ray projection image data values (V(p_q)) comprises the steps of: representing (11) the object attenuation density by a sum of predetermined continuous harmonics (H_ijk(x,y,z)) with unknown coefficients (a_ijk); relating (12) each of the projection image data values to an integral (S(p_q)) of the object attenuation density, and thus to a corresponding sum of sums (a_ijk*H_ijk(p_q)) of the predetermined continuous harmonics with unknown coefficients; determining (13) the unknown coefficients (a_ijk) 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.

Claims

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.

2. The method of claim 1 wherein different ones of said predetermined continuous harmonics represent different spatial frequencies of the attenuation density of said object.

3. The method of claim 1 wherein said predetermined continuous harmonics are any of Newton polynomials, spline interpolating functions, Fourier harmonics, Bessel functions, and Green functions.

4. The method of claim 3 wherein said predetermined continuous harmonics are selected to be of the kind, which minimizes the coupling of equations for given symmetries of object positions.

5. The method of claim 1 wherein said predetermined continuous harmonics is of a number, which is less than the number of said X-ray projection image data values.

6. The method of claim 1 wherein said predetermined continuous harmonics is of a number, which maximizes the signal-to-noise ratio of the reconstructed attenuation density of said object.

7. The method of claim 1 wherein said X-ray projection image data values are obtained from X-ray absorption or transmission measurements, and said integrals of the attenuation density of said object are each an integral along a straight line along which X-rays traveled to produce the related X-ray projection, image data value.

8. The method of claim 7 wherein said X-ray projection image data values are tomosynthesis data values, and said reconstruction is a tomosynthesis reconstruction.

9. The method of claim 7 wherein said X-ray projection image data values are tomographic, PET, or SPECT data values, and said reconstruction is a tomographic, PET, or SPECT reconstruction.

10. The method of claim 1 wherein each said sum of sums of said predetermined continuous harmonics is computed, numerically or analytically, prior to obtaining said X-ray projection image data values.

11. The method of claim 1 wherein said sum of predetermined continuous harmonics with unknown coefficients are selected depending on their estimated signal-to-noise ratio.

12. The method of claim 1 wherein said sum of predetermined continuous harmonics with unknown coefficients are selected depending on the quality of the matrices arising in the equations determining coefficients.

15. A computer program product loadable into the internal memory of a computer, comprising software code portions for performing the method of claim 1 when said product is run on said computer.

13. A method for reconstruction of the attenuation density of an object from X-ray projection image data values, comprising the steps of:

approximating the attenuation density S(x,y,z) of said object by predetermined continuous harmonics H_ijk(x,y,z) with unknown coefficients a_ijk according to S(x,y,z)=Σ

a_ijk*H_ijk(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(p_q) to the attenuation density of said object according to −

ln(V(p_q)=S(P_q), q=1, 2, 3, . . . , where S(P_q) is a sum of attenuation density values of said object;

relating each of said X-ray projection image data values V (P_q) tosaid harmonics according to −

ln (V(P_q))=Σ

a_ijk*H_ijk(P_q) to form a linear equation system, where H_ijk (P_q) is a sum of harmonics corresponding to said sum of attenuation density values of said object;

calculating the unknown coefficients a_ijk by solving said linear equation system; and

reconstructing the attenuation density of said object by calculating S (x, y, z)=Σ

a_ijk*Hi;

k (x, Y, z).

14. The method of claim 13 wherein said X-ray projection image data values are obtained from X-ray transmission measurements, and said sums of attenuation density values S(P_q), p=1, 2, 3, . . . , are each a sum along a respective straight X-ray path from an X-ray source to a pixel of a detector, in which pixel the corresponding X-ray projection image data value was detected.

18. A computer program product loadable into the internal memory of a computer, comprising software code portions for performing the method of claim 13 when said product is run on said computer.

16. An apparatus for reconstruction of the attenuation density of an object from X-ray projection image data values, said apparatus comprising:

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.

17. An X-ray examination system comprising:

the apparatus for reconstruction as claimed in claim 16;

an X-ray detector provided to produce the X-ray projection image data values; and

a display unit for displaying object attenuation density values, wherein

said apparatus for reconstruction is provided (i) to receive the X-ray projection image data values from said X-ray detector, and (ii) to supply data regarding the attenuation density of said object to said display unit.