Computed tomography method and apparatus for acquiring images dependent on a time curve of a periodic motion of the subject

• US 6,665,370 B2
• Filed: 07/09/2002
• Issued: 12/16/2003
• Est. Priority Date: 07/09/2001
• Status: Active Grant

• Current Assignee: Siemens Healthcare GMBH (Siemens AG)
• Original Assignee: Siemens AG
• Inventors: Bruder, Herbert, Flohr, Thomas, Stierstorfer, Karl, Schaller, Stefan, Ohnesorge, Bernd, Mayer, Robert
• Primary Examiner(s): BRUCE, DAVID VERNON
• Application Number:
  US10/191,628
• Publication Number:
  US 20030072419A1
• Time in Patent Office: 525 Days
• Field of Search: 378/4, 378/8, 378/15, 378/901
• US Class Current: 378/15
• CPC Class Codes: A61B 6/027 characterised by the use of a particular data acquisition trajectory, e.g. helical or spiral
• CPC Class Codes: A61B 6/032 Transmission computed tomography [CT]
• CPC Class Codes: A61B 6/4447 Tiltable gantries
• CPC Class Codes: A61B 6/503 for diagnosis of the heart
• CPC Class Codes: G01N 2223/419 computed tomograph
• CPC Class Codes: G01N 2223/612 biological material
• CPC Class Codes: G01N 23/046 using tomography, e.g. computed tomography [CT]

Abstract

In a spiral scan cone beam computed tomography method and apparatus, the output data are divided into sub-segments being shorter than the length required for the reconstruction of a CT image. Segment images having inclined image plane relative to the system axis are reconstructed for the sub-segments. A signal reproducing the time curve of the periodic motion is acquired during the scanning. A z-position on the system axis and a time position with respect to the periodic motion are allocated to the segment images. Segment images belonging to a desired range of z-positions and a desired range of time positions are selected such that the corresponding sub-segments have an overall length adequate for the reconstruction of a CT image. The selected segment images are at least indirectly combined into a resulting CT image with respect to a target image plane.

Claims

1. A method for producing a computed tomography (CT) image comprising the steps of:

(a) scanning a subject, having a region exhibiting a periodic motion, with a conical x-ray beam emanating from a focus and detecting said beam, after attenuation by said subject, with a matrix-like detector array while moving said focus along a spiral path around said subject relative to a system axis, said detector array generating output data dependent on radiation from said x-ray beam that is incident thereon;

(b) dividing said output data, for a segment of said spiral path having a length adequate for reconstructing a CT image, into a plurality of datasets respectively for a plurality of sub-segments of said segment, each of said sub-segments having a length shorter than said length adequate for reconstructing a CT image;

(c) for each of said sub-segments, reconstructing a plurality of segment images having a plane inclined relative to said system axis from the dataset for that sub-segment;

(d) obtaining a signal representing a time curve of said periodic motion during said scanning;

(e) allocating a z-position on said system axis and a time position with respect to said periodic motion to the respective segment images;

(f) selecting segment images within a range of z-positions and a range of time positions so that the respective sub-segments of the selected segment images comprise a total length adequate for reconstruction of a CT image; and

(g) at least indirectly combining the selected segment images to form a resulting CT image with respect to a target image plane.

2. A method as claimed in claim 1 wherein said periodic motion exhibits phases, and step (f) comprises selecting segment images with respective sub-segments arising from a single phase of said periodic motion.

3. A method as claimed in claim 1 wherein said periodic motion exhibits phases, and step (f) comprises selecting segment images with respective sub-segments arising from a plurality of phases of said periodic motion.

4. A method as claimed in claim 1 wherein step (g) comprises directly combining said selected segment images to form said resulting CT image.

5. A method as claimed in claim 4 wherein step (g) comprises directly combining said selected segment images to form said resulting CT image with respect to a target image plane corresponding to the respective z-positions of the selected segment images.

6. A method as claimed in claim 4 wherein said selected segment images have respective z-positions which differ from said target image plane, and comprising the additional step of reformatting said selected segment images into said target image plane before step (g).

7. A method as claimed in claim 1 comprising, for each of said sub-segments, combining the plurality of segment images to form a partial image with respect to said target image plane, and wherein step (g) comprises combining said partial images to form said resulting CT image.

8. A method as claimed in claim 7 comprising employing all segment images for a respective sub-segment to form said partial image.

9. A method as claimed in claim 8 wherein said resulting CT image represents an image of a slice of said subject, and further comprising repeating steps (a) through (g) for successive, adjacent slices of said subject to produce a resulting CT image of a volume of said subject comprising said slices.

10. A method as claimed in claim 9 wherein said successive slices adjoin each other.

11. A method as claimed in claim 7 comprising combining said plurality of segment images to form said partial image by interpolation.

12. A method as claimed in claim 7 comprising combining said plurality of segment images to form said partial image by averaging.

13. A method as claimed in claim 7 comprising combining said plurality of segment images to form said partial image by weighted averaging.

14. A method as claimed in claim 13 comprising weighting said segment images dependent on a desired reconstruction slice thickness of said partial image.

15. A method as claimed in claim 7 comprising selecting a number of said segment images for combining to form said partial image dependent on a desired reconstruction slice thickness of said partial image.

16. A method as claimed in claim 15 comprising reconstructing said segment images with a smallest possible slice thickness.

17. A method as claimed in claim 15 comprising, for each of said sub-segments, selecting said plurality of images to be combined for generating said partial image according to:

18. A method as claimed in claim 7 comprising combining said partial images with respect to a target image plane that intersects said system axis at a right angle.

19. A method as claimed in claim 7 comprising combining said partial images to form said resulting CT image by adding said partial images.

20. A method as claimed in claim 1 comprising reconstructing at least one of said segment images with a curved image plane.

21. A method as claimed in claim 1 wherein step (c) comprises, for each of said sub-segments, reconstructing a plurality of said segment images in image planes that are inclined relative to both a first axis, that intersects said system axis at a right angle by an inclination angle γ

, and a second axis intersecting each of said first axis and said system axis at respective right angles by a tilt angle δ

measured with respect to said system axis.

22. A method as claimed in claim 1 wherein step (b) comprises dividing said output data into sub-segments wherein neighboring sub-segments overlap in overlapping regions, and comprising the additional step of weighting the output data in said overlapping regions so that the respective portions of the output data in said overlap regions belonging to the neighboring sub-segments in that overlap region have respective weightings which, in combination, add to one.

23. A method as claimed in claim 1 wherein step (c) comprises, for each of said sub-segments, reconstructing a plurality of segment images inclined relative to said system axis which have different positions along a z-axis of a Cartesian coordinate system.

24. A method as claimed in claim 23 wherein step (c) further comprises, for each of sub-segments, reconstructing a plurality of images respectively in inclined image planes that intersect in a straight line proceeding tangentially relative to that sub-segment, as said plurality of segment images having a plane inclined relative to said system axis.

25. A method as claimed in claim 23 wherein step (c) comprises, for each of said sub-segments, reconstructing a plurality of said segment images in image planes that are inclined relative to both a first axis, that intersects said system axis at a right angle by an inclination angle γ

, and a second axis intersecting each of said first axis and said system axis at respective right angles by a tilt angle δ

measured with respect to said system axis, and wherein, in step (c), for each of said sub-segments, the plurality of segment images associated therewith respectively have image planes inclined relative to said system axis limited by extreme values δ

_max, and −

δ

_max of said tilt angle δ

, according to $\pm <br><br>{\mathrm{\delta <br><br>}}_{\max }=\arctan <br><br>\left(\frac{-\frac{\mathrm{bM}}{2}\mathrm{Sp}<br><br>\text{\hspace{1em}<br><br>}<br><br>\frac{{\mathrm{\alpha <br><br>}}_1}{2<br><br>\mathrm{\pi <br><br>}}\pm <br><br>\mathrm{RFOV}<br><br>\text{\hspace{1em}<br><br>}<br><br>\cos <br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{\alpha <br><br>}}_1<br><br>\tan <br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{\gamma <br><br>}}_0}{-\frac{R_f}{\cos <br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{\gamma <br><br>}}_0}-\left(\pm <br><br>\mathrm{RFOV}\right)<br><br>\frac{\sin <br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{\alpha <br><br>}}_1}{\cos <br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{\gamma <br><br>}}_0}}\right)$$\mathrm{wherein}$${\mathrm{\gamma <br><br>}}_0=\arctan <br><br>\left(\frac{-\mathrm{Sp}<br><br>\text{\hspace{1em}<br><br>}<br><br>\stackrel{⋒<br><br>}{\mathrm{\alpha <br><br>}}}{2<br><br>\mathrm{\pi <br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>R_f<br><br>\sin <br><br>\text{\hspace{1em}<br><br>}<br><br>\stackrel{⋒<br><br>}{\mathrm{\alpha <br><br>}}}\right).$

26. A method as claimed in claim 1 wherein step (a) comprises rotating said focus around a rotational axis that coincides with said system axis.

27. A method as claimed in claim 1 wherein step (a) comprises rotating said focus around a rotational axis that intersects said system axis at a gantry angle ρ

and wherein, in step (c), for each of said sub-segments, the plurality of segment images have respective inclination angles γ

′

according to ${\mathrm{\gamma <br><br>}}^{\mathrm{\prime <br><br>}}=\arctan <br><br>\text{\hspace{1em}<br><br>}<br><br>\frac{\mathrm{Sp}·<br><br>\cos <br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{\rho <br><br>}}{\sqrt{4<br><br>{\mathrm{\pi <br><br>}}^2·<br><br>R_f{S}^2<br><br>p^{2}4<br><br>\mathrm{\pi <br><br>}·<br><br>R_f<br><br>\cos <br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{\alpha <br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>\sin <br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{\rho <br><br>}·<br><br>\mathrm{Sp}}}.$

28. A method as claimed in claim 27 wherein step (c) comprises, for each of said sub-segments, reconstructing a plurality of said segment images in image planes that are inclined relative to both a first axis, that intersects said system axis at a right angle by an inclination angle γ

, and a second axis intersecting each of said first axis and said system axis at respective right angles by a tilt angle δ

measured with respect to said system axis, and wherein, in step (c), for each of said sub-segments, the plurality of segment images associated therewith respectively have image planes inclined relative to said system axis limited by extreme values δ

_max, and −

δ

_max of said tilt angle δ

, according to $\pm <br><br>{\mathrm{\delta <br><br>}}_{\max }=\arctan <br><br>\left(\frac{-\frac{\mathrm{bM}}{2}\mathrm{Sp}<br><br>\text{\hspace{1em}<br><br>}<br><br>\frac{{\mathrm{\alpha <br><br>}}_1}{2<br><br>\mathrm{\pi <br><br>}}\pm <br><br>\mathrm{RFOV}<br><br>\text{\hspace{1em}<br><br>}<br><br>\cos <br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{\alpha <br><br>}}_1<br><br>\tan <br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{\gamma <br><br>}}_0}{-\frac{R_f}{\cos <br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{\gamma <br><br>}}_0}-\left(\pm <br><br>\mathrm{RFOV}\right)<br><br>\frac{\sin <br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{\alpha <br><br>}}_1}{\cos <br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{\gamma <br><br>}}_0}}\right)$$\mathrm{wherein}$${\mathrm{\gamma <br><br>}}_0=\arctan <br><br>\left(\frac{-\mathrm{Sp}<br><br>\text{\hspace{1em}<br><br>}<br><br>\stackrel{⋒<br><br>}{\mathrm{\alpha <br><br>}}}{2<br><br>\mathrm{\pi <br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>R_f<br><br>\sin <br><br>\text{\hspace{1em}<br><br>}<br><br>\stackrel{⋒<br><br>}{\mathrm{\alpha <br><br>}}}\right),$

and further comprising determining an optimum value γ

_min, of said inclination angle γ

′

for a magnitude of said maximum value of said tilt angle |δ

_max| by satisfying an error criterion.

29. A method as claimed in claim 1 wherein step (c) comprises, for each of said sub-segments, reconstructing a plurality n_ima of segment images inclined relative to said system axis which have different positions along a z-axis of a Cartesian coordinate system, and wherein, $n_{\mathrm{ima}}=\mathrm{floor}$

[sMp]

wherein s is a length of the sub-segment.

30. A method as claimed in claim 29 wherein step (c) comprises, for each of said sub-segments, reconstructing a plurality of said segment images in image planes that are inclined relative to both a first axis, that intersects said system axis at a right angle by an inclination angle γ

, and a second axis intersecting each of said first axis and said system axis at respective right angles by a tilt angle δ

measured with respect to said system axis, and wherein, in step (c), for each of said sub-segments, the plurality of segment images associated therewith respectively have image planes inclined relative to said system axis limited by extreme values δ

_max, and −

δ

_max of said tilt angle δ

, according to $\pm <br><br>{\mathrm{\delta <br><br>}}_{\max }=\arctan <br><br>\left(\frac{-\frac{\mathrm{bM}}{2}\mathrm{Sp}<br><br>\text{\hspace{1em}<br><br>}<br><br>\frac{{\mathrm{\alpha <br><br>}}_1}{2<br><br>\mathrm{\pi <br><br>}}\pm <br><br>\mathrm{RFOV}<br><br>\text{\hspace{1em}<br><br>}<br><br>\cos <br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{\alpha <br><br>}}_1<br><br>\tan <br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{\gamma <br><br>}}_0}{-\frac{R_f}{\cos <br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{\gamma <br><br>}}_0}-\left(\pm <br><br>\mathrm{RFOV}\right)<br><br>\frac{\sin <br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{\alpha <br><br>}}_1}{\cos <br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{\gamma <br><br>}}_0}}\right)$$\mathrm{wherein}$${\mathrm{\gamma <br><br>}}_0=\arctan <br><br>\left(\frac{-\mathrm{Sp}<br><br>\text{\hspace{1em}<br><br>}<br><br>\stackrel{⋒<br><br>}{\mathrm{\alpha <br><br>}}}{2<br><br>\mathrm{\pi <br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>R_f<br><br>\sin <br><br>\text{\hspace{1em}<br><br>}<br><br>\stackrel{⋒<br><br>}{\mathrm{\alpha <br><br>}}}\right)$

and further comprising determining the respective tilt angles δ

of the inclined image planes according to $\mathrm{\delta <br><br>}<br><br>\left(i\right)={\mathrm{\delta <br><br>}}_{\max }<br><br>\frac{2<br><br>i-\left(n_{\mathrm{ima}}-1\right)}{n_{\mathrm{ima}}-1}.$

31. A method as claimed in claim 1 wherein each of said segment images has segment image data associated therewith, and comprising the additional step of compressing said segment image data to form compressed data.

32. A method as claimed in claim 31 wherein the step of compressing said segment image data comprises compressing said segment image data to form compressed data exhibiting a non-uniform pixel matrix having resolution in a first direction, proceeding substantially in a direction of a reference projection for the respective sub-segment is higher than in a second direction proceeding substantially orthogonally relative to said reference projection direction.

33. A method as claimed in claim 32 comprising forming said compressed data of pixels having an oblong shape, with each pixel having a longest extent proceeding substantially in said direction of said reference projection direction for that sub-segment.

34. A method as claimed in claim 33 comprising forming said compressed data of rectangular pixels.

35. A method as claimed in claim 33 comprising converting said segment images into said non-uniform pixel matrix.

36. A method as claimed in claim 33 comprising reconstructing said segment images in said non-uniform pixel matrix.

37. A method as claimed in claim 36 wherein said reconstruction of said segment images ensues by back projection in a back-projection direction, and selecting said back-projection direction to substantially coincide with said reference projection direction for that sub-segment.

38. A method as claimed in claim 31 comprising reversing said compression in step (e) to produce said resulting CT image with a uniform pixel matrix.

39. A method as claimed in claim 38 comprising obtaining said pixels of said uniform matrix by interpolation from the pixels of said non-uniform pixel matrix.

40. A method as claimed in claim 38 comprising obtaining said pixels of said uniform matrix by averaging from the pixels of said non-uniform pixel matrix.

41. A computed tomography (CT) apparatus comprising:

a CT scanner having an x-ray source with a focus and a matrix-like detector array for scanning a subject, having a region exhibiting a periodic motion, with a conical x-ray beam emanating from said focus and detecting said beam, after attenuation by said subject, with said matrix-like detector array while moving said focus along a spiral path around said subject relative to a system axis, said detector array generating output data dependent on radiation from said x-ray beam that is incident thereon;

a signal acquisition unit adapted for interaction with said subject for obtaining a signal from said subject representing said periodic motion;

a computer supplied with said output data and said signal, said computer dividing said output data, for a segment of said spiral path having a length adequate for reconstructing a CT image, into a plurality of datasets respectively for a plurality of sub-segments of said segment, each of said sub-segments having a length shorter than said length adequate for reconstructing a CT image;

said computer, for each of said sub-segments, reconstructing a plurality of segment images having a plane inclined relative to said system axis from the dataset for that sub-segment;

said computer allocating a z-position on said system axis and a time position with respect to said periodic motion to the respective segment images;

said computer selecting segment images within a range of z-positions and a range of time positions so that respective sub-segments for the selected segment images comprise a total length adequate for reconstruction of a CT image; and

said computer combining said selected segment images at least indirectly to form a resulting CT image with respect to a target image plane.

42. A computed tomography apparatus as claimed in claim 41 wherein said periodic motion exhibits phases, and wherein said computer selects segment images with respective sub-segments arising from a single phase of said periodic motion.

43. A computed tomography apparatus as claimed in claim 41 wherein said periodic motion exhibits phases, and wherein said computer selects segment images with respective sub-segments arising from a plurality of phases of said periodic motion.

44. A computed tomography apparatus as claimed in claim 41 wherein said computer directly combines said selected segment images to form said resulting CT image.

45. A computed tomography apparatus as claimed in claim 44 wherein said computer directly combines said selected segment images to form said resulting CT image with respect to a target image plane corresponding to the respective z-positions of the selected segment images.

46. A computed tomography apparatus as claimed in claim 44 wherein said selected segment images have respective z-positions which differ from said target image plane, and wherein said computer reformats said selected segment images into said target image plane before combining said selected segment images to form said resulting CT images.

47. A computed tomography apparatus as claimed in claim 41 wherein said computer, for each of said sub-segments, combines the plurality of segment images to form a partial image with respect to said target image plane, and combines said partial images to form said resulting CT image.

48. A computed tomography apparatus as claimed in claim 47 wherein said computer employs all segment images for a respective sub-segment to form said partial image.

49. A computed tomography apparatus as claimed in claim 48 wherein said resulting CT image represents an image of a slice of said subject, and said computed combines successive, adjacent slices of said subject to produce a resulting CT image of a volume of said subject comprising said slices.

50. A computed tomography apparatus as claimed in claim 49 wherein said successive slices adjoin each other.

51. A computed tomography apparatus as claimed in claim 47 wherein said computer combines said plurality of segment images to form said partial image by interpolation.

52. A computed tomography apparatus as claimed in claim 47 wherein said computer combines said plurality of segment images to form said partial image by averaging.

53. A computed tomography apparatus as claimed in claim 47 wherein said computer combines said plurality of segment images to form said partial image by weighted averaging.

54. A computed tomography apparatus as claimed in claim 43 wherein said computer weights said segment images dependent on a desired reconstruction slice thickness of said partial image.

55. A computed tomography apparatus as claimed in claim 47 wherein said computer selects a number of said segment images for combining to form said partial image dependent on a desired reconstruction slice thickness of said partial image.

56. A computed tomography apparatus as claimed in claim 55 wherein said computer reconstructs said segment images with a smallest possible slice thickness.

57. A computed tomography apparatus as claimed in claim 55 wherein said computer, for each of said sub-segments, selects said plurality of images to be combined for generating said partial image according to:

58. A computed tomography apparatus as claimed in claim 47 wherein said computer combines said partial images with respect to a target image plane that intersects said system axis at a right angle.

59. A computed tomography apparatus as claimed in claim 47 wherein said computer combines said partial images to form said resulting CT image by adding said partial images.

60. A computed tomography apparatus as claimed in claim 47 wherein said computer reconstructs at least one of said segment images with a curved image plane.

61. A computed tomography apparatus as claimed in claim 41 wherein said computer, for each of said sub-segments, reconstructs a plurality of said segment images in image planes that are inclined relative to both a first axis, that intersects said system axis at a right angle by an inclination angle γ

, and a second axis intersecting each of said first axis and said system axis at respective right angles by a tilt angle δ

measured with respect to said system axis.

62. A computed tomography apparatus as claimed in claim 41 wherein said computer divides said output data into sub-segments wherein neighboring sub-segments overlap in overlapping regions, and weighs the output data in said overlap regions so that the respective portions of the output data in said overlapping regions belonging to the neighboring sub-segments in that overlap region have respective weightings which, in combination, add to one.

63. A computed tomography apparatus as claimed in claim 41 wherein said computer, for each of said sub-segments, reconstructs a plurality of segment images inclined relative to said system axis which have different positions along a z-axis of a Cartesian coordinate system.

64. A computed tomography apparatus as claimed in claim 63 wherein said computer, for each of sub-segments, reconstructs a plurality of images respectively in inclined image planes that intersect in a straight line proceeding tangentially relative to that sub-segment, as said plurality of segment images having a plane inclined relative to said system axis.

65. A computed tomography apparatus as claimed in claim 63 wherein said computer, for each of said sub-segments, reconstructs a plurality of said segment images in image planes that are inclined relative to both a first axis, that intersects said system axis at a right angle by an inclination angle γ

, and a second axis intersecting each of said first axis and said system axis at respective right angles by a tilt angle δ

measured with respect to said system axis, and wherein, for each of said sub-segments, the plurality of segment images associated therewith respectively have image planes inclined relative to said system axis limited by extreme values δ

_max, and −

δ

_max of said tilt angle δ

, according to $\pm <br><br>{\mathrm{\delta <br><br>}}_{\max }=\arctan <br><br>\left(\frac{-\frac{\mathrm{bM}}{2}\mathrm{Sp}<br><br>\text{\hspace{1em}<br><br>}<br><br>\frac{{\mathrm{\alpha <br><br>}}_1}{2<br><br>\mathrm{\pi <br><br>}}\pm <br><br>\mathrm{RFOV}<br><br>\text{\hspace{1em}<br><br>}<br><br>\cos <br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{\alpha <br><br>}}_1<br><br>\tan <br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{\gamma <br><br>}}_0}{-\frac{R_f}{\cos <br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{\gamma <br><br>}}_0}-\left(\pm <br><br>\mathrm{RFOV}\right)<br><br>\frac{\sin <br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{\alpha <br><br>}}_1}{\cos <br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{\gamma <br><br>}}_0}}\right)$$\mathrm{wherein}$${\mathrm{\gamma <br><br>}}_0=\arctan <br><br>\left(\frac{-\mathrm{Sp}<br><br>\text{\hspace{1em}<br><br>}<br><br>\stackrel{⋒<br><br>}{\mathrm{\alpha <br><br>}}}{2<br><br>\mathrm{\pi <br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>R_f<br><br>\sin <br><br>\text{\hspace{1em}<br><br>}<br><br>\stackrel{⋒<br><br>}{\mathrm{\alpha <br><br>}}}\right).$

66. A computed tomography apparatus as claimed in claim 41 wherein said focus rotates around a rotational axis that coincides with said system axis.

67. A computed tomography apparatus as claimed in claim 41 wherein said focus rotates around a rotational axis that intersects said system axis at a gantry angle ρ

and wherein, for each of said sub-segments, the plurality of segment images have respective inclination angles γ

′

according to ${\mathrm{\gamma <br><br>}}^{\mathrm{\prime <br><br>}}=\arctan <br><br>\text{\hspace{1em}<br><br>}<br><br>\frac{\mathrm{Sp}·<br><br>\cos <br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{\rho <br><br>}}{\sqrt{4<br><br>{\mathrm{\pi <br><br>}}^2·<br><br>R_f{S}^2<br><br>p^{2}4<br><br>\mathrm{\pi <br><br>}·<br><br>R_f<br><br>\cos <br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{\alpha <br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>\sin <br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{\rho <br><br>}·<br><br>\mathrm{Sp}}}.$

68. A computed tomography apparatus as claimed in claim 67 wherein said computer, for each of said sub-segments, reconstructs a plurality of said segment images in image planes that are inclined relative to both a first axis, that intersects said system axis at a right angle by an inclination angle γ

, and a second axis intersecting each of said first axis and said system axis at respective right angles by a tilt angle δ

measured with respect to said system axis, and wherein, for each of said sub-segments, the plurality of segment images associated therewith respectively have image planes inclined relative to said system axis limited by extreme values δ

_max, and −

δ

_max of said tilt angle δ

, according to $\pm <br><br>{\mathrm{\delta <br><br>}}_{\max }=\arctan <br><br>\left(\frac{-\frac{\mathrm{bM}}{2}\mathrm{Sp}<br><br>\text{\hspace{1em}<br><br>}<br><br>\frac{{\mathrm{\alpha <br><br>}}_1}{2<br><br>\mathrm{\pi <br><br>}}\pm <br><br>\mathrm{RFOV}<br><br>\text{\hspace{1em}<br><br>}<br><br>\cos <br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{\alpha <br><br>}}_1<br><br>\tan <br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{\gamma <br><br>}}_0}{-\frac{R_f}{\cos <br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{\gamma <br><br>}}_0}-\left(\pm <br><br>\mathrm{RFOV}\right)<br><br>\frac{\sin <br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{\alpha <br><br>}}_1}{\cos <br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{\gamma <br><br>}}_0}}\right)$$\mathrm{wherein}$${\mathrm{\gamma <br><br>}}_0=\arctan <br><br>\left(\frac{-\mathrm{Sp}<br><br>\text{\hspace{1em}<br><br>}<br><br>\stackrel{⋒<br><br>}{\mathrm{\alpha <br><br>}}}{2<br><br>\mathrm{\pi <br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>R_f<br><br>\sin <br><br>\text{\hspace{1em}<br><br>}<br><br>\stackrel{⋒<br><br>}{\mathrm{\alpha <br><br>}}}\right),$

and further comprising determining an optimum value γ

_min, of said inclination angle γ

′

for a magnitude of said maximum value of said tilt angle |δ

_max| by satisfying an error criterion.

69. A computed tomography apparatus as claimed in claim 41 wherein said computer, for each of said sub-segments, reconstructs a plurality n_ima of segment images inclined relative to said system axis which have different positions along a z-axis of a Cartesian coordinate system, and wherein, $n_{\mathrm{ima}}=\mathrm{floor}$

[sMp]

wherein s is a length of the sub-segment.

70. A computed tomography apparatus as claimed in claim 69 wherein said computer, for each of said sub-segments, reconstructing a plurality of said segment images in image planes that are inclined relative to both a first axis, that intersects said system axis at a right angle by an inclination angle γ

, and a second axis intersecting each of said first axis and said system axis at respective right angles by a tilt angle δ

measured with respect to said system axis, and wherein, for each of said sub-segments, the plurality of segment images associated therewith respectively have image planes inclined relative to said system axis limited by extreme values δ

_max, and −

δ

_max of said tilt angle δ

, according to $\pm <br><br>{\mathrm{\delta <br><br>}}_{\max }=\arctan <br><br>\left(\frac{-\frac{\mathrm{bM}}{2}\mathrm{Sp}<br><br>\text{\hspace{1em}<br><br>}<br><br>\frac{{\mathrm{\alpha <br><br>}}_1}{2<br><br>\mathrm{\pi <br><br>}}\pm <br><br>\mathrm{RFOV}<br><br>\text{\hspace{1em}<br><br>}<br><br>\cos <br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{\alpha <br><br>}}_1<br><br>\tan <br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{\gamma <br><br>}}_0}{-\frac{R_f}{\cos <br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{\gamma <br><br>}}_0}-\left(\pm <br><br>\mathrm{RFOV}\right)<br><br>\text{\hspace{1em}<br><br>}<br><br>\frac{\sin <br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{\alpha <br><br>}}_1}{\cos <br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{\gamma <br><br>}}_0}}\right)<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{wherein}$${\mathrm{\gamma <br><br>}}_0=\arctan <br><br>\left(\frac{-\mathrm{Sp}<br><br>\text{\hspace{1em}<br><br>}<br><br>\stackrel{⋒<br><br>}{\mathrm{\alpha <br><br>}}}{2<br><br>\mathrm{\pi <br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>R_f<br><br>\sin <br><br>\text{\hspace{1em}<br><br>}<br><br>\stackrel{⋒<br><br>}{\mathrm{\alpha <br><br>}}}\right)$

and further comprising determining the respective tilt angles δ

of the inclined image planes according to $\mathrm{\delta <br><br>}<br><br>\left(i\right)={\mathrm{\delta <br><br>}}_{\max }<br><br>\frac{2<br><br>i-\left(n_{\mathrm{ima}}-1\right)}{n_{\mathrm{ima}}-1}.$

71. A computed tomography apparatus as claimed in claim 41 wherein each of said segment images has segment image data associated therewith, and wherein said computer has a compression stage compressing said segment image data to form compressed data.

72. A computed tomography apparatus as claimed in claim 71 wherein said compression stage compresses said segment image data to form compressed data exhibiting a non-uniform pixel matrix having resolution in a first direction, proceeding substantially in a direction of a reference projection for the respective sub-segment is higher than in a second direction proceeding substantially orthogonally relative to said reference projection direction.

73. A computed tomography apparatus as claimed in claim 72 wherein said compression stage forms said compressed data of pixels having an oblong shape, with each pixel having a longest extent proceeding substantially in said direction of said reference projection direction for that sub-segment.

74. A computed tomography apparatus as claimed in claim 73 wherein said compression stage forms said compressed data of rectangular pixels.

75. A computed tomography apparatus as claimed in claim 73 wherein said computer converts said segment images into said non-uniform pixel matrix.

76. A computed tomography apparatus as claimed in claim 73 wherein said computer reconstructs said segment images in said non-uniform pixel matrix.

77. A computed tomography apparatus as claimed in claim 76 wherein said computer reconstructs said segment images ensues by back projection in a back-projection direction, and selects said back-projection direction to substantially coincide with said reference projection direction for that sub-segment.

78. A computed tomography apparatus as claimed in claim 72 wherein said computer reverses said compression to produce said resulting CT image with a uniform pixel matrix.

79. A computed tomography apparatus as claimed in claim 78 wherein said computer obtains said pixels of said uniform matrix by interpolation from the pixels of said non-uniform pixel matrix.

80. A computed tomography apparatus as claimed in claim 78 wherein said computer obtains said pixels of said uniform matrix by averaging from the pixels of said non-uniform pixel matrix.