3PI algorithm for spiral CT
View Patent ↗Methods and systems for reconstructing images of moving objects being spirally scanned with two dimensional detectors with a 3PI algorithm. The moving objects can be scanned at a rate of up to approximately three times slower than those of pre-existing systems. In a preferred embodiment, the invention allows for a patient on a table moving through a spiral scanner to be slowed down by a factor of up to three, and still use the same size detector array as those in existing spiral scanning systems.
1. A method of reconstructing images from data provided by at least one detector, comprising the steps of:
scanning an object in the spiral fashion with at least one detector that detects at least one cone beam projection, the cone beam projection being wider in the axial direction than projections of four turns of the spiral that are adjacent to a current source position; and
reconstructing an exact image of the scanned object in an efficient manner with a convolution based FBP (Filtered Back Projection) algorithm.
2. The method of claim 1 , wherein the scanning step includes acquiring two-dimensional cone beam (CB) projection data of the object using the detectors.
3. The method of claim 2 , further comprising the step of:
using the detectors substantially similar to those required for a 1PI algorithm.
4. The method of claim 2 , wherein the scanning step further includes the step of:
detecting the cone beam projection being wider in the axial direction as compared to a cone beam projection used in a 1PI algorithm.
5. The method of claim 4 , wherein the scanning step further includes the step of:
detecting the cone beam projection being wider by a factor of at least three times in the axial direction as compared to a cone beam projection used in a 1PI algorithm.
6. The method of claim 1 , wherein the object includes: a person.
7. A method of computing exact images derived from spiral computer tomography scan with area detectors, comprising the steps of:
(a) collecting cone beam (CB) projection data from a detector, which is wider than what is required for a 1PI algorithm; the cone beam covering projections of four turns of the spiral that are adjacent to a current source position;
(b) identifying families of lines on a plane Π intersecting the cone beam projection;
(c) preprocessing the CB projection data;
(d) convolution-filtering said preprocessed CB projection data along said lines;
(e) back projecting said filtered data to form a precursor of said image; and
(f) repeating steps a, b, c, d, e, until an exact image of the object is completed.
8. The method of claim 7 , wherein the scan includes an x-ray exposure of the object.
9. The method of claim 7 , wherein the steps (a)–(f) include:
a 3PI algorithm.
10. A method of computing images derived from computer tomography scan with detectors, comprising the steps of:
(a) collecting cone beam (CB) data from a detector during a scan of an object;
(b) identifying three families of lines on a plane DP(s) intersecting the cone beam, wherein s is value of the parameter describing the scan path and corresponding to the current source position, and the three families of lines include:
(bi) a first family of lines parallel to {dot over (y)}(s), where
{dot over (y)}(s) is the direction of the scan tangent at the current source position;
(bii) a second family of lines tangent to Γ 1 and Γ −1 , where
Γ 1 is the projection of the scan turn defined by s<q<s+2π onto the plane DP(s);
Γ −1 is the projection of the scan turn defined by s−2π<q<s onto the plane DP(s);
q is the parameter along the scan path which describes the point being projected;
(biii) a third family of lines tangent to Γ 2 and Γ −2 , where
Γ 2 is the projection of the scan turn defined by s+2π<q<s+4π onto the plane DP(s);
Γ −2 is the projection of the scan turn defined by s−4π<q<s−2π onto the plane DP(s);
(c) preprocessing and shift invariant filtering said data along said lines of said three families;
(d) back projecting said filtered data to form a precursor of said image; and
(e) repeating steps a, b, c, and d until an image of the object is completed.
11. The method of claim 10 , wherein the preprocessing includes calculation of the derivative of the CB data with respect to source position.
12. The method of claim 10 , wherein the shift invariant filtering includes convolving the said preprocessed data with filter 1/sin γ.
13. The method of claim 10 , wherein back projecting said filtered data from the first family of lines involves multiplying the said filtered data by the coefficient c m =⅔, when the projection of x onto DP(s) is located between L 2 cr and L −2 cr , where
L 2 cr is the line parallel to {dot over (y)}(s) and tangent to Γ 2 ;
L −2 cr is the line parallel to {dot over (y)}(s) and tangent to Γ −2 .
14. The method of claim 10 , wherein back projecting said filtered data from lines in the first family of lines involves multiplying the said filtered data by the coefficient c m =⅓, when the projection of x onto DP(s) is located above L 2 cr or below L −2 cr .
15. The method of claim 10 , wherein back projecting said filtered data from a line in the second family of lines involves multiplying the said filtered data by the coefficient c m =⅔, when the projection of x onto DP(s) is located between Γ 1 and Γ −1 and the point where the line is tangent to Γ 1 ∪Γ −1 is inside the 1PI parametric interval of x.
16. The method of claim 10 , wherein back projecting said filtered data from a line in the second family of lines involves multiplying the said filtered data by the coefficient c m =−⅔, when the projection of x onto DP(s) is located between Γ 1 and Γ −1 and the point where the line is tangent to Γ 1 ∪Γ −1 is outside the 1PI parametric interval of x.
17. The method of claim 10 , wherein back projecting said filtered data from a line in the third family of lines involves multiplying the said filtered data by the coefficient c m =⅓.
18. A method of computing images derived from computer tomography scan with detectors, comprising the steps of:
(a) collecting cone beam data from a detector during a scan of an object;
(b) identifying three families of lines on a plane DP(s) intersecting the cone beam, wherein s is value of a parameter describing the scan path and corresponding to the current source position, and the three families of lines include:
(bi) a first family of lines parallel to {dot over (y)}(s), where
{dot over (y)}(s) is the direction of the scan tangent at the current source position;
(bii) a second family of lines tangent to Γ 1 and Γ −1 , where
Γ 1 is the projection of the scan turn defined by s<q<s+2π onto the plane DP(s);
Γ −1 is the projection of the scan turn defined by s−2π<q<s onto the plane DP(s);
q is the parameter along the scan path which describes the point being projected;
(biii) a third family of lines on the plane DP(s) that have at least three points of intersection s 1 , s 2 , s 3 with Γ ±1 and Γ ±2 , where
Γ 2 is the projection of the scan turn defined by s+2π<q<s+4π onto the plane DP(s);
Γ −2 is the projection of the scan turn defined by s−4π<q<s−2π onto the plane DP(s);
(c) preprocessing and shift invariant filtering said data along said lines of said three families;
(d) back projecting said filtered data to form a precursor of said image; and
(e) repeating steps a, b, c, and d until an image of the object is completed.
19. The method of claim 18 , wherein the points of intersection s 1 , s 2 , s 3 are determined according to the following rules:
s 1 −s =ψ( s 3 −s 2 ) if s+ 2 π<s 3 <s+ 4π,
s 3 −s 2 =ψ( s 1 −s ) if s− 4 π<s 3 <s− 2π,
where ψ(t) is a function with the properties ψ(0)=0ψ′(t)>0, t∈R.
20. The method of claim 18 , wherein the preprocessing includes calculation of the derivative of the CB data with respect to source position.
21. The method of claim 18 , wherein the shift invariant filtering includes convolving the said preprocessed data with filter 1/sin γ.
22. The method of claim 18 , wherein back projecting said filtered data from lines in the first family of lines involves multiplying the said filtered data by the coefficient c m =⅔, when the projection of x onto DP(s) is located between L 2 cr and L −2 cr .
23. The method of claim 18 , wherein back projecting said filtered data from a line in the second family of lines involves multiplying the said filtered data by the coefficient c m =⅔, when the projection of x onto DP(s) is located between Γ 1 and Γ −1 and the point where the line is tangent to Γ 1 ∪Γ −1 is inside the 1PI parametric interval of x.
24. The method of claim 18 , wherein back projecting said filtered data from a line in the second family of lines involves multiplying the said filtered data by the coefficient c m =−⅔, when the projection of x onto DP(s) is located between Γ 1 and Γ −1 and the point where the line is tangent to Γ 1 ∪ Γ −1 is outside the 1PI parametric interval of x.
25. The method of claim 18 , wherein back projecting said filtered data from lines in the third family of lines involves multiplying the said filtered data by the coefficient c m =⅔, when the projection of x onto DP(s) is located above L 2 cr or below L −2 cr .