Methods and apparatus for compensating for view aliasing artifacts

• US 6,438,195 B1
• Filed: 01/26/2001
• Issued: 08/20/2002
• Est. Priority Date: 01/26/2001
• Status: Expired due to Term

• Current Assignee: GE Medical Systems Global Technology Company LLC (GE Healthcare Technologies, Inc.)
• Original Assignee: GE Medical Systems Global Technology Company LLC (GE Healthcare Technologies, Inc.)
• Inventors: Hsieh, Jiang
• Primary Examiner(s): BRUCE, DAVID VERNON
• Application Number:
  US09/771,198
• Time in Patent Office: 571 Days
• Field of Search: 378/4, 378/8, 378/15, 378/62, 378/901
• US Class Current: 378/4
• CPC Class Codes: G06T 2200/12 involving antialiasing
• CPC Class Codes: G06T 2207/10081 Computed x-ray tomography [CT]
• CPC Class Codes: G06T 2207/30004 Biomedical image processing
• CPC Class Codes: G06T 5/50 using two or more images, e.g. averaging or subtraction
• CPC Class Codes: G06T 5/70 Denoising; Smoothing
• CPC Class Codes: Y10S 378/901 Computer tomography program or processor

Abstract

Methods and apparatus to reduce and eliminate aliasing artifacts generated as a result of performing high speed scans are described. In one embodiment, the method includes the steps of applying a weighting function to the projection data, and determining an aliasing index from the weighted data. The aliasing index per view is utilized to determine the region and the amount of synthesized views required to reduce the aliasing artifact.

Claims

1. A method to compensate for view aliasing artifacts in a computed tomography imaging system including an x-ray source for radiating an x-ray beam along an imaging plane toward a detector array including a plurality of detector cells, said method comprising the steps of:

determining a high frequency variation in projection data collected during a scan;

applying a weighting function to the high frequency variation in projection data; and

determining an aliasing index from the weighted data.

2. A method in accordance with claim 1 wherein said step of determining a high frequency variation comprises the step of pre-processing raw data collected during a scan to generate projection data, p(γ

,β

), where γ

is a fan angle, β

is a projection angle.

3. A method in accordance with claim 2 wherein said step of determining a high frequency variation further comprises the step of determining the high frequency variation according to the relationship:

$\mathrm{\xi <br><br>}<br><br>\left(\mathrm{\gamma <br><br>},\mathrm{\beta <br><br>}\right)=\frac{\partial <br><br>p<br><br>\left(\mathrm{\gamma <br><br>},\mathrm{\beta <br><br>}\right)}{\partial <br><br>\mathrm{\beta <br><br>}},$

where γ

is a fan angle, β

is a projection angle, ξ

(γ

,β

) represents the high-frequency variation of the projection.

4. A method in accordance with claim 1 wherein said step of applying a weighting function comprises the step of applying a weighting function, w(γ

,β

), to each high frequency variation of the projection, ξ

(γ

,β

), according to the relationship ξ

(γ

,β

)*w(γ

,β

), where $w<br><br>\left(\mathrm{\gamma <br><br>},\mathrm{\beta <br><br>}\right)=\{\begin{array}{cc}\frac{\mathrm{\gamma <br><br>}-{\mathrm{\gamma <br><br>}}_l<br><br>\left(\mathrm{\beta <br><br>}\right)}{\mathrm{\eta <br><br>}}& {\mathrm{\gamma <br><br>}}_l<br><br>\left(\mathrm{\beta <br><br>}\right)\le <br><br>\mathrm{\gamma <br><br>}<<br><br>{\mathrm{\gamma <br><br>}}_l<br><br>\left(\mathrm{\beta <br><br>}\right)+\mathrm{\eta <br><br>}\\ 1& {\mathrm{\gamma <br><br>}}_l<br><br>\left(\mathrm{\beta <br><br>}\right)\le <br><br>\mathrm{\gamma <br><br>}<<br><br>{\mathrm{\gamma <br><br>}}_h<br><br>\left(\mathrm{\beta <br><br>}\right)\\ \frac{{\mathrm{\gamma <br><br>}}_h<br><br>\left(\mathrm{\beta <br><br>}\right)-\mathrm{\gamma <br><br>}}{\mathrm{\eta <br><br>}}& {\mathrm{\gamma <br><br>}}_h<br><br>\left(\mathrm{\beta <br><br>}\right)-\mathrm{\eta <br><br>}<<br><br>\mathrm{\gamma <br><br>}\le <br><br>{\mathrm{\gamma <br><br>}}_h<br><br>\left(\mathrm{\beta <br><br>}\right)\\ 0& \mathrm{otherwise}.\end{array}$

5. A method in accordance with claim 1 further comprising the step of determining a maximum value of frequency for each view, β

, according to the relationship;

6. A method in accordance with claim 1 wherein said step of determining an aliasing index comprises the step of determining for each view, β

, a preliminary aliasing index, ε

(β

), from the weighted data.

7. A method in accordance with claim 6 wherein said step of determining an aliasing index further comprises the step of scaling the preliminary aliasing index by a number of views per rotation, v, a reconstruction location, R, and a reconstruction filter kernel, φ

.

8. A method in accordance with claim 7 wherein said step of determining an aliasing index further comprises the step of applying a low pass filter to the scaled preliminary aliasing index.

9. A method in accordance with claim 1 further comprising the step of utilizing the aliasing index to determine a region and an amount of synthesized views required to reduce aliasing artifacts.

10. A method in accordance with claim 1 further comprising the step of utilizing the aliasing index to control an amount of contribution of synthesized view weighting to minimize potential aliasing artifact.

11. A method in accordance with claim 1 further comprising the step of utilizing the aliasing index to predict sampling rates as a function of a projection angle, when a DAS sampling rate is dynamically adjusted.

12. An imaging system comprising a computer, a gantry having a detector array, an x-ray source for radiating an x-ray beam along an imaging plane toward the detector array including a plurality of detector cells, the computer coupled to the x-ray source and the gantry, said imaging system configured to:

determine a high frequency variation in data collected during a scan;

apply a weighting function to said high frequency variation in projection data; and

determine an aliasing index from said weighted data.

13. An imaging system in accordance with claim 12 wherein said imaging system further configured to pre-process raw data collected during a scan to generate projection data, p(γ

,β

), where γ

is a fan angle, β

is a projection angle.

14. An imaging system according to claim 13 wherein said imaging system further configured to determine a high frequency variation in said projection data according to the relationship:

$\mathrm{\xi <br><br>}<br><br>\left(\mathrm{\gamma <br><br>},\mathrm{\beta <br><br>}\right)=\frac{\partial <br><br>p<br><br>\left(\mathrm{\gamma <br><br>},\mathrm{\beta <br><br>}\right)}{\partial <br><br>\mathrm{\beta <br><br>}},$

where γ

is a fan angle, β

is a projection angle, and ξ

(γ

,β

) represents said high frequency variation of the projection.

15. An imaging system according to claim 12 wherein said imaging system further configured to apply a weighting function, w(γ

,β

), to each high frequency variation of the projection, ξ

(γ

,β

), according to the relationship ξ

(γ

,β

)*w(γ

,β

), where $w<br><br>\left(\mathrm{\gamma <br><br>},\mathrm{\beta <br><br>}\right)=\{\begin{array}{cc}\frac{\mathrm{\gamma <br><br>}-{\mathrm{\gamma <br><br>}}_l<br><br>\left(\mathrm{\beta <br><br>}\right)}{\mathrm{\eta <br><br>}}& {\mathrm{\gamma <br><br>}}_l<br><br>\left(\mathrm{\beta <br><br>}\right)\le <br><br>\mathrm{\gamma <br><br>}<<br><br>{\mathrm{\gamma <br><br>}}_l<br><br>\left(\mathrm{\beta <br><br>}\right)+\mathrm{\eta <br><br>}\\ 1& {\mathrm{\gamma <br><br>}}_l<br><br>\left(\mathrm{\beta <br><br>}\right)\le <br><br>\mathrm{\gamma <br><br>}<<br><br>{\mathrm{\gamma <br><br>}}_h<br><br>\left(\mathrm{\beta <br><br>}\right)\\ \frac{{\mathrm{\gamma <br><br>}}_h<br><br>\left(\mathrm{\beta <br><br>}\right)-\mathrm{\gamma <br><br>}}{\mathrm{\eta <br><br>}}& {\mathrm{\gamma <br><br>}}_h<br><br>\left(\mathrm{\beta <br><br>}\right)-\mathrm{\eta <br><br>}<<br><br>\mathrm{\gamma <br><br>}\le <br><br>{\mathrm{\gamma <br><br>}}_h<br><br>\left(\mathrm{\beta <br><br>}\right)\\ 0& \mathrm{otherwise}.\end{array}$

16. An imaging system according to claim 12 wherein said imaging system further configured to determine a maximum value of frequency for each view, β

, according to the relationship;

17. An imaging system according to claim 12 wherein said imaging system further configured to determine for each view, β

, a preliminary aliasing index, ε

(β

), from said weighted data.

18. An imaging system according to claim 17 wherein said imaging system further configured to scale said preliminary aliasing index by a number of views per rotation, v, a reconstruction location, R, and a reconstruction filter kernel, φ

.

19. An imaging system according to claim 18 wherein said imaging system further configured to apply a low pass filter to said scaled preliminary aliasing index.

20. An imaging system according to claim 12 wherein said aliasing index is utilized to determine a region and an amount of synthesized views required to reduce aliasing artifacts.

21. An imaging system according to claim 12 wherein said aliasing index is utilized to control an amount of contribution of synthesized view weighting to minimize potential aliasing artifact.

22. An imaging system according to claim 12 wherein said aliasing index is utilized to predict sampling rates as a function of a projection angle, when a DAS sampling rate is dynamically adjusted.

23. A processor programmed to compensate for view aliasing artifacts in a computed tomography imaging system, said processor configured to:

acquire projection data;

apply a weighting function to a high frequency variation in said projection data;

determine an aliasing index from said weighted data; and

reduce aliasing artifacts using said aliasing index per view.

24. A processor in accordance with claim 23 wherein said processor further configured to pre-process raw data collected during a scan to generate projection data p(γ

,β

), where γ

is a fan angle, β

is a projection angle.

25. A processor in accordance with claim 24 wherein said processor further configured to determine a high frequency variation of a projection according to the relationship:

$\mathrm{\xi <br><br>}<br><br>\left(\mathrm{\gamma <br><br>},\mathrm{\beta <br><br>}\right)=\frac{\partial <br><br>p<br><br>\left(\mathrm{\gamma <br><br>},\mathrm{\beta <br><br>}\right)}{\partial <br><br>\mathrm{\beta <br><br>}},$

where γ

is a fan angle, β

is a projection angle, and ξ

(γ

,β

) represents said high frequency variation of the projection.

26. A processor in accordance with claim 23 wherein said processor further configured to apply a weighting function, w(γ

,β

), to each high frequency variation of the projection, ξ

(γ

,β

), according to the relationship ξ

(γ

,β

)*w(γ

,β

), $\mathrm{where}<br><br>\text{\hspace{1em}<br><br>}<br><br>w<br><br>\left(\mathrm{\gamma <br><br>},\mathrm{\beta <br><br>}\right)=\{\begin{array}{cc}\frac{\mathrm{\gamma <br><br>}-{\mathrm{\gamma <br><br>}}_l<br><br>\left(\mathrm{\beta <br><br>}\right)}{\mathrm{\eta <br><br>}}& {\mathrm{\gamma <br><br>}}_l<br><br>\left(\mathrm{\beta <br><br>}\right)\le <br><br>\mathrm{\gamma <br><br>}<<br><br>{\mathrm{\gamma <br><br>}}_l<br><br>\left(\mathrm{\beta <br><br>}\right)+\mathrm{\eta <br><br>}\\ 1& {\mathrm{\gamma <br><br>}}_l<br><br>\left(\mathrm{\beta <br><br>}\right)\le <br><br>\mathrm{\gamma <br><br>}<<br><br>{\mathrm{\gamma <br><br>}}_h<br><br>\left(\mathrm{\beta <br><br>}\right)\\ \frac{{\mathrm{\gamma <br><br>}}_h<br><br>\left(\mathrm{\beta <br><br>}\right)-\mathrm{\gamma <br><br>}}{\mathrm{\eta <br><br>}}& {\mathrm{\gamma <br><br>}}_h<br><br>\left(\mathrm{\beta <br><br>}\right)-\mathrm{\eta <br><br>}<<br><br>\mathrm{\gamma <br><br>}\le <br><br>{\mathrm{\gamma <br><br>}}_h<br><br>\left(\mathrm{\beta <br><br>}\right)\\ 0& \mathrm{otherwise}.\end{array}$

27. A processor in accordance with claim 23 wherein said processor configured to determine a maximum value of frequency for each view, β

, according to the relationship;

28. A processor in accordance with claim 23 wherein said processor configured to determine for each view, β

, a preliminary aliasing index, ε

(β

), from said weighted data.

29. A processor in accordance with claim 28 wherein said processor configured to scale said preliminary aliasing index by at least one of a number of views per rotation, v, a reconstruction location, R, and a reconstruction filter kernel, φ

.

30. A processor in accordance with claim 29 wherein said processor configured to apply a low pass filter to said scaled preliminary aliasing index.

31. A processor in accordance with claim 23 wherein said aliasing index is utilized to determine a region and an amount of synthesized views required to reduce aliasing artifacts.

32. A processor in accordance with claim 23 wherein said aliasing index is utilized to control an amount of contribution of synthesized view weighting to minimize potential aliasing artifact.

33. A processor in accordance with claim 23 wherein said aliasing index is utilized to predict sampling rates as a function of a projection angle, when a DAS sampling rate is dynamically adjusted.

34. A computer-readable medium in an imaging system, said computer-readable medium comprising:

a function to determine a high frequency variation in projection data;

a weighting function applied to said high frequency variation of the projection data; and

a function to determine a maximum frequency value for each view of projection data.

35. A computer-readable medium according to claim 34 wherein said projection data comprises pre-process raw data collected during a scan configured to generate projection data, high frequency function uses projection data p(γ

,β

), where γ

is a fan angle, β

, is a projection angle.

36. A computer-readable medium according to claim 34 wherein said function to determine high frequency variation of projection data comprises the relationship:

$\mathrm{\xi <br><br>}<br><br>\left(\mathrm{\gamma <br><br>},\mathrm{\beta <br><br>}\right)=\frac{\partial <br><br>p<br><br>\left(\mathrm{\gamma <br><br>},\mathrm{\beta <br><br>}\right)}{\partial <br><br>\mathrm{\beta <br><br>}},$

where γ

is a fan angle, β

is a projection angle, and ξ

(γ

,β

) represents said high frequency variation of the projection.

37. A computer-readable medium according to claim 34 wherein said weighting function comprises:

$w<br><br>\left(\mathrm{\gamma <br><br>},\mathrm{\beta <br><br>}\right)=\{\begin{array}{cc}\frac{\mathrm{\gamma <br><br>}-{\mathrm{\gamma <br><br>}}_l<br><br>\left(\mathrm{\beta <br><br>}\right)}{\mathrm{\eta <br><br>}}& {\mathrm{\gamma <br><br>}}_l<br><br>\left(\mathrm{\beta <br><br>}\right)\le <br><br>\mathrm{\gamma <br><br>}<<br><br>{\mathrm{\gamma <br><br>}}_l<br><br>\left(\mathrm{\beta <br><br>}\right)+\mathrm{\eta <br><br>}\\ 1& {\mathrm{\gamma <br><br>}}_l<br><br>\left(\mathrm{\beta <br><br>}\right)\le <br><br>\mathrm{\gamma <br><br>}<<br><br>{\mathrm{\gamma <br><br>}}_h<br><br>\left(\mathrm{\beta <br><br>}\right)\\ \frac{{\mathrm{\gamma <br><br>}}_h<br><br>\left(\mathrm{\beta <br><br>}\right)-\mathrm{\gamma <br><br>}}{\mathrm{\eta <br><br>}}& {\mathrm{\gamma <br><br>}}_h<br><br>\left(\mathrm{\beta <br><br>}\right)-\mathrm{\eta <br><br>}<<br><br>\mathrm{\gamma <br><br>}\le <br><br>{\mathrm{\gamma <br><br>}}_h<br><br>\left(\mathrm{\beta <br><br>}\right)\\ 0& \mathrm{otherwise}.\end{array}$

38. A computer-readable medium according to claim 37 wherein said weighting function, w(γ

,β

), is configured to be applied to each high frequency variation of the projection, ξ

(γ

,β

), according to the relationship ξ

(γ

,β

)*w(γ

,β

).

39. A computer-readable medium according to claim 34 wherein said function to determine a maximum frequency value comprises: