Tomography signal processing system

• US 4,135,247 A
• Filed: 08/15/1977
• Issued: 01/16/1979
• Est. Priority Date: 08/15/1977
• Status: Expired due to Term

• Current Assignee: Siemens AG
• Original Assignee: Siemens AG
• Inventors: Gordon, Bernard M., Neumann, Leopold, Dobbs, John McG.
• Primary Examiner(s): Wise, Edward J.
• Application Number:
  US05/824,632
• Time in Patent Office: 519 Days
• Field of Search: 364/414, 364/518, 364/515, 364/527, 250/369, 250/445 T
• US Class Current: 378/11
• CPC Class Codes: A61B 6/032 Transmission computed tomography [CT]
• 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 2211/421 Filtered back projection [FBP]
• CPC Class Codes: Y10S 378/901 Computer tomography program or processor

Abstract

A tomography processor system for processing data from a plurality of projections in essentially real time to produce a reconstructed image immediately following completion of a scan. The system includes specialized high-speed processing stages for performing required calculations and operating in concert with a low-cost computer providing overall system control. These processing stages form a multi-stage pipeline processor capable of performing the correction, convolution, interpolation, and back projection functions required to reconstruct the desired final image. The invention makes use of a reconstruction algorithm particularly adapted to implementation in the manner disclosed and claimed.

Claims

1. In a tomography system for exposing a body to radiation to provide image data representative of the density of the body in a cross-sectional plane, of the type having:

source means for providing radiation passing through the body;

detector means for receiving the radiation passing through the body along a plurality of paths and for providing output signals representative of radiation intensity received; and

scanning means for providing for rotation of the source and detector means with respect to said body and for periodically causing emission of radiation from the source means during said rotation to provide a scan having a plurality of projections at a corresponding plurality of projection angles;

the tomography processor comprising;

corrector means for correcting the output signals from the detector means to provide corrected data points, each representative of a line integral of the density of the body along the path traversed by the radiation producing the corresponding detector means output signal;

first memory means for storing the corrected data points from a projection and for retrieving the stored, corrected data points from a projection at a later time;

convolver means for convolving with a deblurring function the corrected data points from a projection, retrieved by the first memory means, to produce a plurality of convolved data points from a projection;

second memory means, coupled to the convolver means, for storing the convolved data points from a projection and for retrieving the stored, convolved data points from a projection at a later time;

image memory means for storing data representative of the density of the body in said cross-sectional plane and having a plurality of memory locations each for storing a value representative of the density of a corresponding area of the body in said cross-sectional plane;

reconstructor means, coupled to said second memory means, and operative in response to data retrieved by said second memory means, for back-projecting the convolved data points from a projection by determining the corresponding convolved data point for each location in image memory and adding data derived from the corresponding convolved data point to the value stored in that location in image memory.

2. The tomography processor of claim 1 further comprising:

control means for sequentially activating the corrector and convolver, so as to process the data from each projection in a scan to produce a plurality of convolved data points from each projection and for activating the reconstructor means to back-project the convolved data from each projection in a scan to produce data in each location in the image memory means representative of the density of the corresponding area of the body.

3. The tomography processor of claim 2 wherein each of the first and second memory means includes a two-bank memory, comprising:

a first memory bank;

a second memory bank; and

means for storing data in a first one of said first and second memory banks and for retrieving data from the second one of said first and second memory banks in response to a selection signal designating in which bank data is to be stored and from which bank data is to be retrieved;

the tomography processor further including;

means for providing selection signals to the first memory means so that corrected data points from a projection may be stored therein while corrected data points from a prior projection may be concurrently retrieved therefrom; and

means for providing selection signals to the second memory means so that convolved data points from a projection may be stored therein while convolved data points from a prior projection may be concurrently retrieved therefrom.

4. The tomography processor of claim 3 wherein the reconstructor means further includes means for multiplying each convolved data point by a weighting factor to provide the data to be added to the value stored in the corresponding location in image memory.

5. The tomography processor of claim 4 wherein the corrector means includes means for performing calculations to compensate for previously measured errors between the output signals produced by the detector means and the actual intensity of radiation received thereby, and to compensate for beam-hardening of the radiation passing through the body.

6. The tomography processor of claim 5 wherein the source means provides a fan-beam of radiation.

7. The tomography processor of claim 3 further including third memory means for storing the detector means output signals from a projection and for retrieving the stored output signals during a subsequent projection.

8. The tomography processor of claim 3 wherein the corrector, convolver, and reconstructor means each compose stages of a pipeline processor, and wherein the first and second memory means, and the image memory means compose intermediate storage sections of a pipeline processor;

and

wherein the tomography processor includes means for controlling each of the intermediate memory sections and for causing each of the pipeline processor stages to sequentially process the data points from each projection stored in and retrieved by the previous intermediate memory section to produce data points stored by the following intermediate memory section to produce the final image data.

9. The tomography processor of claim 4 wherein the source means provides a fan-beam of radiation passing through the body;

and

wherein the detector means includes a plurality of detectors, each for detecting radiation intensity and for producing an output signal representative thereof, located along a semi-circle having a center located at the source, each of the detector means being located at a respective detector angle with respect to a line passing through the source means and the axis of rotation.

10. The tomography processor of claim 9 wherein the corrector means further includes means for multiplying the output signal from each of the detectors by the cosine of the detector angle of the detector producing the respective output signal to produce the corrected data points.

11. The tomography processor of claim 10 wherein the weighting factor by which the reconstructor means multiplies the convolved data points is equal to the reciprocal of the square of the distance from the source means to the area of the body corresponding with the location in image memory in which the weighted and convolved data point is to be stored.

12. The tomography processor of claim 2 wherein the control means includes a programmable, digital processor.

13. The tomography processor of claim 12 further comprising:

corrector activation means, operative in response to a corrector activation signal, for causing the corrector to begin correcting the output signals from a projection from the detector means and to cease correcting output signals from the detector means when all of the output signals from a projection have been corrected;

convolver activation means, operative in response to a convolver activation signal for causing the convolver to begin convolving corrected data points from a projection and for causing the convolver to cease convolving corrected data points when all the corrected data points from a projection have been convolved; and

reconstructor activation means, operative in response to a reconstructor activation signal for causing the reconstructor to begin back-projecting the convolved data points from a projection and for causing the reconstructor to cease back-projecting the convolved data from a projection when all of the convolved data points from a projection have been back-projected; and

wherein the corrector, convolver, and reconstructor activation signals are provided by the control means.

14. The tomography processor of claim 13 wherein the corrector means is directly coupled to the first memory means and wherein the first memory means is directly coupled to the convolver means.

15. A fan-beam tomography system for providing data representative of the density of a body in a cross-sectional plane, comprising:

source means for emitting a fan-beam of radiation passing through the body;

detector means for receiving radiation passing through the body along a plurality of paths and for providing corresponding output signals representative of radiation intensity received along each of said paths;

scanning means for providing for relative rotation about an axis of the source and detector means with respect to the body and for causing the source means to emit radiation during said rotation to provide a scan made up of a plurality of projections at a corresponding plurality of projection angles;

the detector means including a plurality of detectors, each for detecting radiation intensity and for producing an output signal representative thereof, located along a semi-circle having a center located at the source, each of the detectors being located at a respective detector angle with respect to a line passing through the source means and the axis of rotation;

corrector means for receiving each of the output signals from the detector means and for providing in response thereto, a corresponding corrected data point representative of a line integral of the density of the body along the corresponding path of the radiation received by the detector means, including;

means for performing calculations to compensate for previously measured errors between the output signals produced by the detector means and the actual intensity of radiation received thereby and to compensate for beam-hardening of the radiation passing through the body; and

means for multiplying the output signal from each of the detectors by the cosine of the respective detector angle to provide the corrected data points;

first memory means for storing the corrected data points from a projection and for retrieving the stored, corrected data points from a projection at a later time;

convolver means for convolving with a deblurring function the corrected data points from a projection, retrieved by the first memory means, to produce a plurality of convolved data points from a projection;

second memory means, coupled to the convolver means, for storing the convolved data points from a projection and for retrieving the stored, convolved data points from a projection at a later time;

an image memory having a plurality of memory locations each for storing a value representative of the density of a corresponding area of the body in the cross-sectional plane; and

reconstructor means, coupled to said second memory means, and operative in response to data retrieved by said second memory means, for back-projecting the convolved data points from a projection, including;

address means for sequentially providing address data for accessing each of the locations in image memory during each projection;

locator means, responsive to data derived from said address data, for determining which of the convolved data points from a projection corresponds with the presently accessed image memory location;

means for multiplying the corresponding data point determined by said locator means by a weighting factor to produce a weighted data point; and

means for adding the weighted data point to the value, resulting from prior projections, stored in the presently accessed image memory location and for storing the sum thereof in the presently accessed memory location to replace the value resulting from prior projections.

16. The tomography system of claim 15 further comprising control means including:

means for sequentially causing the corrector and convolver means to process the data from each projection in a scan to produce a plurality of convolved data points from each projection; and

means for causing the reconstructor means to reconstruct the convolved data points from each projection in a scan to produce data in each location in the image memory representative of the density of the corresponding area of the body.

17. The tomography system of claim 15 wherein the weighting factor by which the reconstructor means multiplies the convolved data point is equal to the reciprocal of the square of the distance from the source means to the area of the body corresponding with the accessed location in image memory.

18. The tomography system of claim 17 wherein the fan-beam of radiation includes x-rays.

19. The tomography system of claim 18 further comprising control means including:

means for sequentially causing the corrector and convolver means to process the data from each projection in a scan to produce a plurality of convolved data points from each projection; and

means for causing the reconstructor means to reconstruct the convolved data points from each projection in a scan to produce data in each location in the image memory representative of the density of the corresponding area of the body.

20. The tomography system of claim 19 wherein the control means includes a programmable, digital processor.

21. The tomography system of claim 17 wherein each of the plurality of image memory locations is associated with an area of the body, the address of each location also being representative of coordinates of the associated body area in an image memory coordinate system fixed with respect to the body;

and

wherein the reconstructor means further includes transformation means, operative in response to address data from the address means, for providing data representative of projection system coordinates, in a coordinate system fixed with respect to the radiation source and detector means, of the body area associated with the presently accessed image memory location.

22. The tomography system of claim 21 wherein the control means further includes means for providing projection angle data representative of the angle between the projection coordinate system and the image memory coordinate system;

and

wherein the transformation means includes means responsive to the projection angle data for adding incremental values to the data representative of projection system coordinates of the image memory location previously accessed to produce data representative of the projection system coordinates of the body area associated with the presently accessed image memory location.

23. The tomography system of claim 21 wherein the convolver means further includes interpolation means, responsive to the plurality of convolved data points for providing interpolated data points corresponding with paths lying between the paths for which the detector means provides corresponding output signals, so that the data points from said convolver means include convolved data points each corresponding with a path for which the detector means provides an output signal, and interpolated data points corresponding with paths lying between the paths for which the detector means produces an output signal.

24. A fan-beam tomography system for providing data representative of the density of a body in a cross-sectional plane, comprising:

source means for emitting a fan-beam of radiation passing through the body;

detector means for receiving radiation passing through the body along a plurality of paths and for providing corresponding output signals representative of radiation intensity received along each of said paths;

scanning means for providing for relative rotation about an axis of the source and detector means with respect to the body and for causing the source means to emit pulses of radiation during said rotation to provide a scan made up of a plurality of projections at a corresponding plurality of projection angles;

the detector means including;

a plurality of detectors each for detecting radiation intensity and for producing an output signal representative thereof;

a plurality of integrators, each associated with a respective one of said detectors, for integrating the output signal of the associated detector during each projection to produce an integrated detector output signal representative of the integral of the output signal during each projection from the associated detector; and

conversion means, responsive to each of the integrated detector output signals for providing detector means output signals representative of the inverse of the logarithm of each of the integrated detector output signals;

corrector means for receiving each of the output signals from the detector means and for providing in response thereto, a corresponding corrected data point representative of a line integral of the density of the body along the corresponding path of the radiation received by the detector means, including;

means for performing calculations to compensate for previously measured errors between the output signals produced by the detector means and the actual intensity of radiation received thereby;

first memory means for storing the corrected data points from a projection and for retrieving the stored, corrected data points from a projection at a later time;

convolver means for convolving with a deblurring function the corrected data points from a projection, retrieved by the first memory means, to produce a plurality of convolved data points from a projection;

second memory means, coupled to the convolver means, for storing the convolved data points from a projection and for retrieving the stored, convolved data points from a projection at a later time;

an image memory having a plurality of memory locations each for storing a value representative of the denstiy of a corresponding area of the body in the cross-sectional plane; and

reconstructor means, coupled to said second memory means and operative in response to data retrieved by the second memory means, for back-projecting the convolved data points from a projection, including;

address means for sequentially providing address data accessing each of the locations in image memory during each projection;

locator means, responsive to data derived from said address data, for determining which of the convolved data points from a projection corresponds with the presently accessed image memory location;

means for multiplying the corresponding data point determined by said locator means by a weighting factor to produce a weighted data point; and

means for adding the weighted data point to the value, resulting from prior projections, stored in the presently accessed image memory location and for storing the sum thereof in the presently accessed image memory location to replace the value resulting from prior projections.

25. The tomography system of claim 24 wherein the conversion means includes at least one logarithmic analog-to-digital converter for providing digital representations of the integrated detector output signals.

26. The tomography system of claim 25 wherein the integrators each include integrators having an auto-zero mode for reducing drift errors therein.

27. The tomography system of claim 26 including means for selecting auto-zero mode for each of the integrators prior to the emission of each pulse of radiation from the source means.

28. The tomography system of claim 26 further comprising means for multiplexing the integrated detector output signals so that the integrated detector output signals are serially provided to the at least one logarithmic converter for conversion to digital form.

29. The tomography system of claim 28 further including means for causing each integrator to enter auto-zero mode substantially immediately after the output signal therefrom is converted to digital form by the analog-to-digital converter.

30. The tomography system of claim 29 wherein the plurality of detectors is arranged in a linear array and wherein said multiplexing means provides the integrated detector output signals to said converter in a sequence in which the integrated detector output signals are provided in the order in which their respective associated detectors are located in the linear array, beginning with detectors located in the center of the array and proceeding to the ends of the array.

31. The tomography system of claim 25 wherein said corrector means is directly coupled to said first memory means and wherein said first memory means is directly coupled to said convolver means.

32. The tomography system of claim 24 wherein each of the plurality of image memory locations is associated with an area of the body, the address of each location also being representative of coordinates of the associated body area in an image memory coordinate system fixed with respect to the body;

and

wherein the reconstructor means further includes transformation means, operative in response to address data from the address means, for providing data representative of projection system coordinates, in a coordinate system fixed with respect to the radiation source and detector means, of the body area associated with the presently accessed image memory location.

33. The tomography system of claim 32 wherein the transformation means includes means for adding incremental values to the data representative of projection system coordinates of the image memory location previously accessed to produce data representative of the projection system coordinates of the body area associated with the presently accessed image memory location;

wherein the body areas associated with the image memory location are arranged along orthogonal rows and columns;

and further comprising;

means for providing projection-angle data representative of the angle between the projection coordinate system and the image memory coordinate system; and

means responsive to the projection-angle data for providing to the transformation means data representative of δ

·

sin θ and

δ

·

cos θ

values, where δ

is the distance along the rows and columns between adjacent body areas and θ

is the projection angle, for determining said incremental values.

34. A fan-beam tomography system for providing data representative of the density of a body in a cross-sectional plane, comprising:

source means for emitting a fan-beam of radiation passing through the body;

detector means for receiving radiation passing through the body along a plurality of paths and for providing corresponding output signals representative of radiation intensity received along each of said paths;

scanning means for providing for relative rotation about an axis of the source and detector means with respect to the body and for causing the source means to emit radiation during said rotation to provide a scan made up of a plurality of projections at a corresponding plurality of projection angles;

corrector means for receiving each of the output signals from the detector means and for providing in response thereto, a corresponding corrected data point representative of a line integral of the density of the body along the corresponding path of the radiation received by the detector means, including;

means for performing calculations to compensate for previously measured errors between the output signals produced by the detector means and the actual intensity of radiation received thereby;

first memory means for storing the corrected data points from a projection and for retrieving the stored, corrected data points from a projection at a later time;

convolver means for convolving with a deblurring function the corrected data points from a projection, retrieved by the first memory means, to produce a plurality of convolved data points from a projection;

second memory means, coupled to the convolver means, for storing the convolved data points from a projection and for retrieving the stored, convolved data points from a projection at a later time;

an image memory having a plurality of memory locations, each for storing a value representative of the density of an associated area of the body in the cross-sectional plane, each of the plurality of image memory locations being associated with an area of the body, the address of each location also being representative of coordinates of the associated body area in an image memory coordinate system fixed with respect to the body;

reconstructor means, coupled to said second memory means, and operative in response to data retrieved by said second memory means, for back-projecting the convolved data points from a projection, including;

address means for sequentially providing address data for accessing each of the locations in image memory during each projection;

transformation means, operative in response to address data from the address means, for performing a two-dimensional coordinate transformation to provide data representative of projection system coordinates in a coordinate system fixed with respect to the radiation source and detector means, of the body area associated with the presently accessed image memory location;

locator means, responsive to projection system coordinate data from said transformation means, for determining which of the convolved data points from a projection corresponds with the presently accessed image memory location;

means for multiplying the corresponding data point determined by said locator means by a weighting factor to produce a weighted data point; and

means for adding the weighted data point to the value, resulting from prior projections, stored in the presently accessed image memory location and for storing the sum thereof in the presently accessed memory location to replace the value resulting from prior projections.

35. The tomography system of claim 34 further comprising control means, including:

means for sequentially causing the corrector and convolver means to process the data from each projection in a scan to produce a plurality of convolved data points from each projection;

means for causing the reconstructor means to reconstruct the convolved data points from each projection in a scan to produce data in each location in the image memory representative of the density of the corresponding area of the body; and

means for providing projection angle data representative of the angle between the projection coordinate system and the image memory coordinate system; and

wherein the transformation means includes means responsive to the projection angle data for adding incremental values to the data representative of projection system coordinates of the image memory location previously accessed to produce data representative of the projection system coordinates of the body area associated with the presently accessed image memory location.

36. The tomography system of claim 35 wherein the body areas associated with the image memory locations are arranged along orthogonal rows and columns so that the image memory coordinate system is a two-dimensional Cartesian coordinate system.

37. The tomography system of claim 34 wherein the transformation means includes means for adding incremental values to the data representative of projection system coordinates of the image memory location previously accessed to produce data representative of the projection system coordinates of the body area associated with the presently accessed image memory location.

38. The tomography system of claim 37 wherein the body areas associated with the image memory location are arranged along orthogonal rows and columns, and further comprising:

means for providing projection-angle data representative of the angle between the projection coordinate system and the image memory coordinate system; and

means responsive to the projection-angle data for providing to the transformation means data representative of δ

·

sin θ and

δ

·

cos θ

values, where δ

is the distance along the rows and columns between adjacent body areas and θ

is the projection angle, for determining said incremental values.

39. The tomography system of claim 38 wherein the means for providing data representative of δ

·

sin θ and

δ

·

cos θ

values includes a programmable, digital processor.

40. The tomography system of claim 39 wherein the digital processor provides δ

·

sin θ and

δ

·

cos θ

values for a projection during a previous projection.

41. The tomography system of claim 38 wherein the locator means includes a read-only memory for storing data representative of a locator function associating each location in image memory with one of the paths corresponding with the convolved data points.

42. The tomography system of claim 41 wherein the locator means read-only memory provides data representative of coefficients of a two-dimensional piece-wise linear expansion of the locator function as a function of the projection system coordinates of the presently accessed image memory location;

and

wherein the locator means further includes means for multiplying the projection system coordinate data from the transformation means by the expansion coefficients provided by the locator factor read-only memory and for adding the products thereof to provide the locator function value.

43. The tomography system of claim 38 wherein the corrector means is directly coupled to the first memory means and wherein the first memory means is directly coupled to the convolver means.

44. The tomography system of claim 37 wherein the means for multiplying includes a weighting factor means, responsive to data from the transformation means, for producing the weighting factor.

45. The tomography system of claim 44 wherein the weighting factor means includes a read-only memory responsive to the projection system coordinate data from said transformation means for providing at its output, data representative of the weighting factor.

46. The tomography system of claim 45 wherein the weighting factor by which the reconstructor means multiplies the convolved data point is equal to the reciprocal of the square of the distance from the source means to the area of the body corresponding with the presently accessed location in image memory.

47. The tomography system of claim 45 wherein the weighting factor means read-only memory provides data representative of coefficients of a two-dimensional piece-wise quadratic expansion of the weighting factor as a function of the projection system coordinates of the presently accessed image memory location;

and

wherein the weighting factor means further includes means for multiplying the projection system coordinate data from the transformation means by the expansion coefficients provided by the weighting factor read-only memory and for adding the products thereof to provide the weighting factor.

48. The tomography system of claim 45 further comprising:

locator read-only memory means responsive to projection sysem coordinates from the transformation means for providing output signals representative of which input data point contains data representative of the body area associated with the image memory location presently addressed by the address means.

49. The tomography system of claim 48 wherein the locator means read-only memory and the weighting means read-only memory produce output data representative of the coefficients of mathematic expansions, in terms of the projection system coordinates, providing data respectively representative of the data point selected by the locator means and the weighting factor provided by the weighting means.

50. The tomography system of claim 34:

wherein the convolver means further includes interpolation means, responsive to the plurality of convolved data points for providing interpolated data points corresponding with paths lying between the paths for which the detector means provides corresponding output signals, so that the data points from said convolver means include convolved data points each corresponding with a path for which the detector means provides an output signal, and interpolated data points corresponding with paths lying between the paths for which the detector means produces an output signal; and

wherein the locator means includes means, operative in response to data from said transformation means, for selecting from among said convolved data points and said interpolated data points the data point having a corresponding path passing most closely to center of the area of the body corresponding with the presently accessed image memory location.

51. For use in a fan-beam tomography system having a source of radiation and means for detecting radiation for providing data representative of the density of a body in a cross-sectional plane, of the type having a corrector, a convolver, and an image reconstructor respectively interconnected by two intermediate, two-bank memories and operative as a multistage pipeline processor to provide a plurality of convolved data points from each of a plurality of tomographic projections in response to data from said detecting means, an image reconstructor for performing back projection of the plurality of convolved data points taken during each of the plurality of projections, comprising:

an image memory having a plurality of memory locations each associated with an area of the body in the cross-sectional plane, for storing data representative of the density of the associated body area, each location having an address, the address of each location also being representative of coordinates of the associated body area in an image memory coordinate system fixed with respect to the body;

address means for providing address data to the image memory for accessing each of the memory locations during each projection;

transformation means, operative in response to address data from the address means, for providing data representative of projection system coordinates, in a coordinate system fixed with respect to the radiation source and detecting means, of the body area associated with the presently accessed image memory location;

locator means, operative in response to the projection system coordinate data from the transformation means, for selecting from among the convolved data points, the convolved data point having data representative of the density of the body area associated with the image memory location presently accessed by the address means; and

means for adding the value stored in the presently accessed image memory location to data derived from the convolved data point selected by the locator means, and for storing the sum thereof in the presently accessed image memory location to replace the previously stored value.

52. The image reconstructor of claim 51 wherein the address means includes means for sequentially providing address data representative of adjacent body areas;

and

wherein the transformation means includes means for adding incremental values to the data representative of the projection system coordinates of the image memory location previously accessed to produce data representative of the projection system coordinates of the body area associated with the presently accessed image memory location.

53. The image reconstructor of claim 52 wherein the body areas associated with the image memory location are arranged along orthogonal rows and columns, and further comprising:

means for providing projection-angle data representative of the angle between the projection coordinate system and the image memory coordinate system;

means responsive to the projection-angle data for providing data representative of δ

·

sin θ and

δ

·

cos θ

values, where δ

is the distance along the rows and columns between adjacent body areas and θ

is the projection angle; and

wherein the means for adding includes means for selectively adding the δ

·

sin θ and

the δ

·

cos θ

to the data representative of the projection system coordinates of the image memory location previously accessed.

54. The image reconstructor of claim 53 wherein the means for providing data representative of δ

·

sin θ and

δ

·

cos θ

values includes a programmable, digital processor.

55. The image reconstructor of claim 54 wherein the digital processor provides δ

·

sin θ and

δ

·

cos θ

values for a projection during a previous projection.

56. The image reconstructor of claim 51 further including:

weighting means, operative in response to the projection system coordinate data, for providing a weighting factor;

means for multiplying the weighting factor and the data point selected by the locator means to provide a weighted data point;

the weighted data point being added by the means for adding to the value stored in the presently addressed image memory location.

57. The image reconstructor of claim 56 wherein the weighting factor is equal to the reciprocal of the square of the distance between the source of radiation and the body area associated with the presently addressed image memory location.

58. The image reconstructor of claim 56 wherein the weighting means includes a read-only memory responsive to the projection system coordinate data from said transformation means for providing at its output, data representative of the weighting factor.

59. The image reconstructor of claim 58 wherein the weighting factor by which the reconstructor means multiplies the convolved data point is equal to the reciprocal of the square of the distance from the source means to the area of the body corresponding with the presently accessed location in image memory.

60. The image reconstructor of claim 58 wherein the weighting factor means read-only memory provides data representative of coefficients of a two-dimensional piece-wise quadratic expansion of the weighting factor as a function of the projection system coordinates of the presently accessed image memory location;

and

wherein the weighting factor means further includes means for multiplying the projection system coordinate data from the transformation means by the expansion coefficients provided by the weighting means read-only memory and for adding the products thereof to provide the weighting factor.

61. The image reconstructor of claim 58 further comprising:

locator read-only memory means responsive to projection system coordinates from the transformation means for providing output signals representative of which convolved data point contains data representative of the body area associated with the image memory location presently accessed by the address means.

62. The image reconstructor of claim 61 wherein the locator means read-only memory and the weighting means read-only memory produce output data representative of coefficients of mathematical expansions, in terms of the projection system coordinates, providing data respectively representative of the data point selected by the locator means and the weighting factor provided by the weighting factor.

63. The image reconstructor of claim 51 wherein the locator means includes a read-only memory for storing data representative of a locator function associating each location in image memory with one of the paths corresponding with the convolved data points.

64. The image reconstructor of claim 63 wherein the locator means read-only memory provides data representative of coefficients of a two-dimensional piece-wise linear expansion of the locator function as a function of the projection system coordinates of the presently accessed image memory location;

and

wherein the locator means further includes means for multiplying the projection system coordinate data from the transformation means by the expansion coefficients provided by the locator means read-only memory and for adding the products thereof to provide the locator function value.

65. In a fan-beam tomography system for exposing a body to radiation to provide data representative of the density of the body in a cross-sectional plane, of the type having:

source means for providing radiation for passage through the body;

detector means for receiving the radiation passing through the body along a plurality of paths and for providing output signals representative of radiation intensity received, and scanning means for providing rotation of the source and detector means with respect to said body and for causing emission of radiation from the source means during said rotation to provide a scan having a plurality of projections at a corresponding plurality of projection angles;

the method of processing the detector means output signals, comprising the steps of;

correcting the output signals from the detector means to provide corrected data points, each representative of a line integral of the density of the body along the path traversed by the radiation producing the corresponding detector means output signal;

storing in a first memory the corrected data points from a projection;

retrieving from the first memory the stored, corrected data points from a projection after all the corrected data points from that projection have been stored;

convolving with a deblurring function the corrected data points from a projection, retrieved from the first memory, to produce a plurality of convolved data points from a projection;

storing the convolved data points from a projection in a second memory;

retrieving from the second memory the stored, convolved data points from a projection after all the convolved data points from the projection have been stored;

providing an image memory having a plurality of memory locations corresponding with a similar plurality of areas of the body in said plane, for storing data representative of the density of the corresponding area of the body; and

back-projecting the convolved data points from a projection retrieved by said second memory by;

sequentially accessing each location in the image memory;

determining the corresponding convolved data point for the presently accessed location in image memory;

multiplying the previously-determined corresponding convolved data point by a weighting factor to provide a weighted data point;

adding the weighted data point to the value stored in the presently accessed location in the image memory; and

storing the results of the adding step in the presently accessed location in the image memory to replace the value previously stored therein;

repeating the preceeding steps to correct, convolve, and back-project the data from each projection in a scan to produce data in each location in the image memory representative of the density of the corresponding area of the body;

wherein each of the first and second memories includes a two-bank memory, having a first memory bank and a second memory bank;

wherein the steps of storing and retrieving in said first and second memories include the steps of storing data in a first one of said first and second memory banks in the respective memories and concurrently retrieving data from the second one of said first and second memory banks in the respective memories in response to a selection signal designating in which bank data is to be stored and from which bank data is to be retrieved; and

wherein the step of repeating includes the step of providing selection signals for the first memory so that corrected data points from a projection may be stored in one bank thereof while corrected points from a prior projection may be retrieved from the other bank thereof.

66. The method of claim 65 further including the step of:

prior to exposing the body to radiation to provide data representative of the densities thereof and without said body between the source means and the detector means, causing emission of radiation from the source means and measuring the output signals from the detector means to determine errors between the output signals produced by the detector means and the actual intensity of radiation received thereby;

and wherein the step of correcting includes the step of performing calculations to compensate for the previously determined errors, and to compensate for beam-hardening of the radiation passing through the body.

67. The method of claim 66 wherein the step of correcting further includes the step of multiplying each convolved data point by a weighting factor prior to storing the convolved data point in the corresponding location in image memory.

68. The method of claim 67 further including the step of storing output signals from the detector means from a projection and retrieving the stored output signals during a subsequent projection.