Method for statistically reconstructing images from a plurality of transmission measurements having energy diversity and image reconstructor apparatus utilizing the method

• US 6,754,298 B2
• Filed: 02/18/2003
• Issued: 06/22/2004
• Est. Priority Date: 02/20/2002
• Status: Expired due to Term

• Current Assignee: Board of Regents of the University of Michigan (University of Michigan)
• Original Assignee: Board of Regents of the University of Michigan (University of Michigan)
• Inventors: Fessler, Jeffrey A.
• Primary Examiner(s): BRUCE, DAVID VERNON
• Application Number:
  US10/368,534
• Publication Number:
  US 20030156684A1
• Time in Patent Office: 490 Days
• Field of Search: 378/4, 378/8, 378/15, 378/19, 378/94
• US Class Current: 378/4
• CPC Class Codes: A61B 6/032 Transmission computed tomography [CT]
• CPC Class Codes: A61B 6/4035 the source being combined with a filter or grating
• CPC Class Codes: A61B 6/405 Source units specially adapted to modify characteristics of the beam during the data acquisition process A61B6/4021, A61B6/4035 take precedence
• CPC Class Codes: A61B 6/4241 using energy resolving detectors, e.g. photon counting
• CPC Class Codes: A61B 6/482 involving multiple energy imaging
• 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 2207/10081 Computed x-ray tomography [CT]
• CPC Class Codes: G06T 2211/408 Dual energy
• CPC Class Codes: G06T 2211/424 Iterative
• CPC Class Codes: G06T 5/70 Denoising; Smoothing

Abstract

A method for statistically reconstructing images from a plurality of transmission measurements having energy diversity and image reconstructor apparatus utilizing the method are provided. A statistical (maximum-likelihood) method for dual-energy X-ray CT accommodates a wide variety of potential system configurations and measurement noise models. Regularized methods (such as penalized-likelihood or Bayesian estimations) are straightforward extensions. One version of the algorithm monotonically decreases the negative log-likelihood cost function each iteration. An ordered-subsets variation of the algorithm provides a fast and practical version. The method and apparatus provide material characterization and quantitatively accurate CT values in a variety of applications. The method and apparatus provide improved noise/dose properties.

Claims

1. A method for statistically reconstructing images from a plurality of transmission measurements having energy diversity, the method comprising:

providing a plurality of transmission measurements having energy diversity; and

processing the measurements with an algorithm based on a statistical model which accounts for the energy diversity to obtain at least one final component image which has reduced noise.

2. The method as claimed in claim 1, further comprising providing a cost function based on the statistical model wherein the cost function is minimized during the step of processing.

3. The method as claimed in claim 2, wherein the cost function has a gradient which is calculated during the step of processing.

4. The method as claimed in claim 3, wherein the gradient is calculated by backprojecting.

5. The method as claimed in claim 1, further comprising analyzing the at least one final component image.

6. The method as claimed in claim 1, further comprising calibrating spectra of the measurements to obtain calibration data wherein the step of processing utilizes the calibration data.

7. The method as claimed in claim 1, further comprising displaying the at least one final component image.

8. The method as claimed in claim 3, wherein the gradient is calculated by approximately using a subset of the measurements, such as an ordered subset of projection views, to accelerate the algorithm.

9. The method as claimed in claim 2, wherein the cost function has a regularizing penalty term.

10. The method as claimed in claim 1, wherein the measurements are dual-energy X-ray CT scans.

11. The method as claimed in claim 1, wherein the measurements are transmission scans with differing energy spectra, such as X-ray sources with different tube voltages or different filtrations, or gamma-ray sources with multiple energies.

12. The method as claimed in claim 2, wherein the cost function includes a log-likelihood term.

13. The method as claimed in claim 2, wherein the cost function consists solely of a log-likelihood function, which is called maximum likelihood reconstruction, or wherein the cost function consists of both a log-likelihood function and a regularizing penalty function, which is called penalized-likelihood or maximum a posteriori image reconstruction.

14. The method as claimed in claim 1, further comprising preprocessing the measurements prior to the step of processing to obtain preprocessed measurements and wherein the preprocessed measurements are processed in the step of processing to obtain the at least one component image.

15. The method as claimed in claim 12, wherein the log likelihood term is a function that depends on a model for an ensemble mean of the transmission measurements, and the model incorporates characteristics of an energy spectrum.

16. The method as claimed in claim 12, wherein the log-likelihood term is a function of the transmission measurements, prior to any pre-processing such as taking a logarithm of the measurements.

17. The method as claimed in claim 3, wherein the gradient of the cost function is calculated using a parametric approximation, such as polynomials, tables, or piecewise polynomials.

18. The method as claimed in claim 9, wherein the regularizing penalty term is based on quadratic functions of linear combinations of voxel values or nonquadratic (edge-preserving) functions of such combinations.

19. The method as claimed in claim 2, wherein parameter constraints such as non-negativity of voxel values are enforced during or after minimization of the cost function.

20. The method as claimed in claim 14, wherein the processing step is based on the preprocessed measurements and uses a cost function based on a statistical model for variability of the preprocessed measurements.

21. An image reconstructor apparatus for statistically reconstructing images from a plurality of transmission measurements having energy diversity, the apparatus comprising;

means for providing a plurality of transmission measurements having energy diversity; and

means for processing the measurements with an algorithm based on a statistical model which accounts for the energy diversity to obtain at least one final component image which has reduced noise.

22. The apparatus as claimed in claim 21, further comprising means for providing a cost function based on the statistical model wherein the cost function is minimized by the means for processing.

23. The apparatus as claimed in claim 22, further comprising means for calculating a gradient of the cost function.

24. The apparatus as claimed in claim 23, wherein the means for calculating calculates the gradient by backprojecting.

25. The apparatus as claimed in claim 21, further comprising means for analyzing the at least one final component image.

26. The apparatus as claimed in claim 21, further comprising means for calibrating spectra of the measurements to obtain calibration data wherein the means for processing utilizes the calibration data.

27. The apparatus as claimed in claim 21, further comprising a display for displaying the at least one final component image.

28. The apparatus as claimed in claim 23, wherein the means for calculating calculates the gradient approximately using a subset of the measurements, such as an ordered subset of projection views, to accelerate the algorithm.

29. The apparatus as claimed in claim 22, wherein the cost function has a regularizing penalty term.

30. The apparatus as claimed in claim 21, wherein the measurements are transmission scans with differing energy spectra, such as X-ray sources with different tube voltages or different filtrations, or gamma-ray sources with multiple energies.

31. The apparatus as claimed in claim 21, wherein the cost function includes a log-likelihood term.

32. The apparatus as claimed in claim 22, wherein the cost function consists solely of a log-likelihood function, which is called maximum likelihood reconstruction, or wherein the cost function consists of both a log-likelihood function and a regularizing penalty function, which is called penalized-likelihood or maximum a posteriori image reconstruction.

33. The apparatus as claimed in claim 22, wherein the cost function includes a maximum likelihood or penalized likelihood algorithm.

34. The apparatus as claimed in claim 21, further comprising means for preprocessing the measurements to obtain preprocessed measurements wherein the preprocessed measurements are processed by the means for processing to obtain the at least one component image.

35. The apparatus as claimed in claim 31, wherein the log likelihood term is a function that depends on a model for an ensemble mean of the transmission measurements, and the model incorporates characteristics of an energy spectrum.

36. The apparatus as claimed in claim 31, wherein the log-likelihood term is a function of the transmission measurements, prior to any preprocessing such as taking a logarithm of the measurements.

37. The apparatus as claimed in claim 23, wherein the gradient of the cost function is calculated using a parametric approximation, such as polynomials, tables, or piecewise polynomials.

38. The apparatus as claimed in claim 29, wherein the regularizing penalty term is based on quadratic functions of linear combinations of voxel values or nonquadratic (edge-preserving) functions of such combinations.

39. The apparatus as claimed in claim 22, wherein parameter constraints such as non-negativity of voxel values are enforced during or after minimization of the cost function.

40. The apparatus as claimed in claim 34, wherein the means for processing processes the preprocessed measurements and uses a cost function based on a statistical model for variability of the preprocessed measurements.