Methods and apparatus for correcting scatter

• US 6,633,626 B2
• Filed: 02/01/2002
• Issued: 10/14/2003
• Est. Priority Date: 02/01/2002
• Status: Expired due to Fees

• Current Assignee: General Electric Company
• Original Assignee: General Electric Company
• Inventors: Trotter, Dinko E. Gonzalez, Claus, Bernhard Erich Hermann, Muller, Serge Louis Wilfrid
• Primary Examiner(s): BRUCE, DAVID VERNON
• Application Number:
  US10/062,338
• Publication Number:
  US 20030147491A1
• Time in Patent Office: 620 Days
• Field of Search: 378/37, 378/62, 378/98, 378/98.2, 378/901
• US Class Current: 378/62
• CPC Class Codes: A61B 6/00 Apparatus or devices for radiation diagnosis; Apparatus or devices for radiation diagnosis combined with radiation therapy equipment instruments measuring radiation intensity for application in the field of nuclear medicine, e.g. in vivo counting, G01T1/161; apparatus for taking X-ray photographs G03B42/02
• CPC Class Codes: A61B 6/502 for diagnosis of breast, i.e. mammography
• CPC Class Codes: A61B 6/5282 due to scatter
• CPC Class Codes: A61B 6/583 using calibration phantoms
• CPC Class Codes: G01N 23/04 and forming images of the material
• CPC Class Codes: G01N 23/044 using laminography or tomosynthesis

Abstract

A method for removing scatter in an image includes acquiring data of an object of interest, and using an iterative equation including a thickness-dependent kernel modulation factor to reconstruct an image of the object.

Claims

1. A method for removing scatter in an image, said method comprising:

acquiring data of an object of interest; and

using an iterative equation including a thickness-dependent kernel modulation factor to reconstruct an image of the object.

2. A method in accordance with claim 1 wherein said using the iterative equation including a thickness-dependent kernel modulation factor comprises using a thickness-dependent modulation factor α

_k in accordance with;

$a_k=\frac{{\stackrel{\_}{p}}_k}{{\stackrel{\_}{p}}_{k_0}},$

where;

{overscore (p)}_k is a norm of a scatter kernel p; and

{overscore (p)}_k0 is a norm of a scatter kernel for a compression thickness of the object.

3. A method in accordance with claim 1 further comprising estimating a kernel re-normalization map for use in the iterative equation.

4. A method in accordance with claim 3 wherein estimating the kernel re-normalization map comprises estimating the re-normalization map according to N(m)˜

e<sup>μ

d_b(m)</sup>;

where;

N(m) is the re-normalization map of a pixel m;

μ

is a mean attenuation coefficient for an X-ray photon spectrum in breast equivalent material; and

d_b(m) is a distance between pixel m and a closest pixel belonging to an object boundary.

5. A method in accordance with claim 3 wherein estimating the kernel re-normalization map for use in the iterative equation comprises incorporating the kernel re-normalization map into the iterative equation b⁽ⁿ⁾ according to:

$b^{\left(n\right)}=\frac{y}{2^l}+\left(\frac{2^l-1}{2^l}\right)<br><br>b^{\left(n-1\right)}-\frac{N<br><br>\text{\hspace{1em}<br><br>}<br><br>p*{\mathrm{ab}}_1^{\left(n-1\right)}}{2^l}-\frac{p*{\mathrm{ab}}_2^{\left(n-1\right)}}{2^l}.$

where;

y is a measured image;

p is a scatter kernel;

{overscore (P)}_k is a norm of a scatter kernel p;

l is an integer that satisfies the condition {overscore (p)}<

2^l;

subscript 1 is the direct events outside of the object boundary;

subscript 2 is the direct events inside the object boundary;

α

is the kernel modulation factor;

N is the kernel re-normalization map;

bⁿ is an estimate of the image formed by directly transmitted photons; and

n is a quantity of iterations.

6. A method in accordance with claim 3 wherein estimating a re-normalization map for use in the iterative equation comprises estimating a re-normalization map for each pixel outside of the breast boundary by calculating a distance between the pixel and a closest pixel belonging to the breast boundary.

7. A method in accordance with claim 1 wherein using an iterative equation including a thickness-dependent kernel modulation comprises using an iterative equation including a compressed breast thickness-dependent kernel modulation factor to reconstruct an image of the object.

8. A method in accordance with claim 1 further comprising subtracting a scatter signal estimate from a measured image during each iteration.

9. A method in accordance with claim 8 wherein subtracting a scatter signal estimate comprises subtracting a scatter signal estimate generated using at least one convolution.

10. A method in accordance with claim 9 wherein using at least one convolution comprises using at least one convolution computed in Fourier space.

11. A method in accordance with claim 9 wherein using at least one convolution comprises using two one-dimensional convolutions.

12. A method in accordance with claim 1 further comprising estimating a scatter signal and using the scatter signal estimate in a scatter correction algorithm to estimate a direct image.

13. A medical imaging system for removing scatter in an image, said medical imaging system comprising:

a detector array;

at least one radiation source; and

a computer coupled to said detector array and radiation source and configured to;

acquire data of an object of interest;

estimate a re-normalization map according to N(m)˜

e<sup>μ

d_b(m)</sup>;

where;

N(m) is the re-normalization map of a pixel m;

μ

is a mean attenuation coefficient for an X-ray photon spectrum in

breast equivalent material; and

d_b(m) is a distance between pixel m and a closest pixel belonging to an object boundary;

use an iterative equation including a thickness-dependent kernel modulation factor in accordance with $a_k=\frac{{\stackrel{\_}{p}}_k}{{\stackrel{\_}{p}}_{k_0}},$

 

where;

{overscore (p)}_k is a norm of a scatter kernel p; and

{overscore (p)}_k00 is a norm of a scatter kernel for a compression thickness of the object; and

incorporate the re-normalization map into the iterative equation b⁽ⁿ⁾ according to;

$b^{\left(n\right)}=\frac{y}{2^l}+\left(\frac{2^l-1}{2^l}\right)<br><br>b^{\left(n-1\right)}-\frac{N<br><br>\text{\hspace{1em}<br><br>}<br><br>p*{\mathrm{ab}}_1^{\left(n-1\right)}}{2^l}-\frac{p*{\mathrm{ab}}_2^{\left(n-1\right)}}{2^l}.$

 

where;

y is a measured image;

p is a scatter kernel;

{overscore (p)}_k is a norm of a scatter kernel p;

l is an integer that satisfies the condition {overscore (p)}<

2^l;

subscript 1 is the direct events outside of the object boundary;

subscript 2 is the direct events inside the object boundary;

α

is the kernel modulation factor;

N is the kernel re-normalization map;

bⁿ is an estimate of the image formed by directly transmitted photons; and

n is a quantity of iterations.

14. A method for removing scatter in an image, said method comprising:

acquiring data of an object of interest; and

using an iterative equation to reconstruct an image of the object when a scatter fraction is greater than approximately 0.5.

15. A method in accordance with claim 14 further comprising:

defining an initial scatter kernel estimation;

re-defining an initial (zeroth estimate) of a direct image

re-defining the direct image; and

defining an initial direct estimation using the initial scatter kernel estimation and the re-defined direct image.

16. A method in accordance with claim 14 further comprising selecting a quantity l such that {overscore (p)}<

2^l;

where;

{overscore (p)} is the scatter kernel norm; and

l is an integer that satisfies the condition {overscore (p)}<

2^l.

17. A method in accordance with claim 14 further comprising selecting an iterative equation such that:

b⁽⁰⁾=y−

S⁽⁰⁾, is an initial estimate, with

b⁽ⁿ⁾=α

·

b<sup>(n−

1)</sup>+(1−

α

)·

(y−

p*b<sup>(n−

1)</sup>), is an iterative update, where

s⁽⁰⁾=p*y.

wherein;

y is a measured image;

p is a scatter kernel;

α

is the kernel modulation factor;

N is the kernel re-normalization map;

bⁿ is an estimate of the image formed by directly transmitted photons; and

n is a quantity of iterations.

18. A method in accordance with claim 17 further comprising selecting α

such that $\frac{\stackrel{\_}{p}-1}{\stackrel{\_}{p}+1}<<br><br>\mathrm{\alpha <br><br>}<<br><br>1.$

19. A method in accordance with claim 17 further comprising selecting α

such that $\mathrm{\alpha <br><br>}=1-\frac{2}{{\hat{p}}_{\min }+{\hat{p}}_{\max }+2},$

where {circumflex over (p)}_max={overscore (p)} and {circumflex over (p)}_min are the maximum and minimum values, respectively, of {circumflex over (p)}, the Fourier transform of p.

20. A method in accordance with claim 15 wherein defining an initial scatter estimation comprises defining an initial scatter estimation s₍₀₎ in accordance with $s^{\left(0\right)}=\frac{p*y}{1+\stackrel{\_}{p}}=\frac{p*\left(b+p*b\right)}{1+\stackrel{\_}{p}}=\frac{p*b*(\delta }{}$

+p)1+p_,

where;

y is a measured image;

δ

is the Kronecker delta function;

p is a scatter kernel;

{overscore (p)} is a scatter kernel norm;

l is an integer that satisfies the condition {overscore (p)}<

2^l; and

b is a direct image.

21. A method in accordance with claim 15 wherein defining an initial direct estimation comprises defining an initial direct estimation in accordance with $b^{\left(n\right)}=\frac{b}{2^l}+\frac{p*b}{2^l}+(\frac{2^l-1}{2^l}$

 



δ

-p2l)*b(n-1),

where;

δ

is the Kronecker delta function;

p is a scatter kernel;

n is a quantity of iterations;

l is an integer that satisfies the condition {overscore (p)}<

2^l; and

bⁿ is an estimate of the image formed by directly transmitted photons.

22. A method in accordance with claim 15 wherein re-defining a direct image comprises re-defining a direct image in accordance with b⁽⁰⁾=y−

s⁽⁰⁾,

where;

b is a direct image;

S is a scatter image; and

y is an image including the direct image and the scatter image.

23. A computer readable medium encoded with a program executable by a computer for removing scatter from an image, said program configured to instruct the computer to:

acquire data of an object of interest;

define an initial scatter signal estimation in accordance with $s^{\left(0\right)}=\frac{p*y}{1+\stackrel{\_}{p}}=\frac{p*\left(b+p*b\right)}{1+\stackrel{\_}{p}}=\frac{p*b*\left(\mathrm{\delta <br><br>}+p\right)}{1+\stackrel{\_}{p}},$

 

where;

y is a measured image;

δ

is the Kronecker delta function;

p is a scatter kernel;

{overscore (p)} is a scatter kernel norm;

l is an integer that satisfies the condition {overscore (p)}<

2^l;

b is a direct image;

re-define a direct image;

define an initial direct estimation in accordance with $b^{\left(n\right)}=\frac{b}{2^l}+\frac{p*b}{2^l}+\left(\frac{2^l-1}{2^l}<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{\delta <br><br>}-\frac{p}{2^l}\right)*b^{\left(n-1\right)};<br><br>$

 

where;

n is a quantity of iterations;

use an iterative equation to reconstruct an image of the object when a scatter fraction is greater than approximately 0.5; and

select a sub-iteration quantity l such that {overscore (p)}<

2^l.

25. A computer readable medium in accordance with claim 23 wherein to use the iterative equation including a thickness-dependent kernel modulation factor, said program configured to use a thickness-dependent modulation factor α

_k in accordance with;

$a_k=\frac{{\stackrel{\_}{p}}_k}{{\stackrel{\_}{p}}_{k_0}},$

where;

{overscore (p)}_k is a norm of a scatter kernel p; and

{overscore (p)}_k0 is a norm of a scatter kernel for a compression thickness of the object.

26. A computer readable medium in accordance with claim 23 wherein said program further configured to estimate a re-normalization map for use in the iterative equation.

27. A computer readable medium in accordance with claim 25 wherein to estimate the re-normalization map, said computer further configured to estimate the re-normalization map according to N(m)˜

e<sup>μ

d_b(m)</sup>;

where;

N(m) is the re-normalization map of a pixel m;

μ

is a mean attenuation coefficient for an X-ray photon spectrum in breast equivalent material; and

d_b(m) is a distance between pixel m and a closest pixel belong to an object boundary.

28. A computer readable medium in accordance with claim 25 wherein to estimate the re-normalization map for use in the iterative equation, said program further configured to incorporate the re-normalization map into the iterative equation b⁽ⁿ⁾according to:

$b^{\left(n\right)}=\frac{y}{2^l}+\left(\frac{2^l-1}{2^l}\right)<br><br>b^{\left(n-1\right)}-\frac{N<br><br>\text{\hspace{1em}<br><br>}<br><br>p*{\mathrm{ab}}_1^{\left(n-1\right)}}{2^l}-\frac{p*{\mathrm{ab}}_2^{\left(n-1\right)}}{2^l}.$

where;

p is a scatter kernel;

l is an integer that satisfies the condition {overscore (p)}<

2^l;

subscript 1 is the direct events outside of the object boundary;

subscript 2 is the direct events inside the object boundary;

α

is the kernel modulation factor;

N is the kernel re-normalization map;

bⁿ is an estimate of the image formed by directly transmitted photons; and

n is a quantity of iterations.

29. A computer readable medium in accordance with claim 25 wherein to estimate a re-normalization map for use in the iterative equation, said program further configured to estimate a re-normalization map for each pixel outside of the breast boundary by calculating a distance between the pixel and a closest pixel belonging to the breast boundary.

24. A computer readable medium encoded with a program executable by a computer for removing scatter from an image, said program configured to instruct the computer to:

acquire data of an object of interest; and

use an iterative equation including a thickness-dependent kernel modulation factor to reconstruct an image of the object.

30. A medical imaging system for removing scatter in an image, said medical imaging system comprising:

a detector array;

at least one radiation source; and

a computer coupled to said detector array and radiation source and configured to;

acquire data of an object of interest; and

use an iterative equation to reconstruct an image of the object when a scatter fraction is greater than approximately 0.5.

31. A medical imaging system in accordance with claim 30 wherein said computer further configured to:

define an initial scatter kernel estimation;

re-define a direct image; and

define an initial direct estimation using the initial scatter kernel estimation and the re-defined direct image.

32. A medical imaging system in accordance with claim 30 wherein said computer further configured to select a quantity l such that {overscore (p)}<

2^l;

where;

{overscore (p)} is the scatter kernel norm; and

l is an integer that satisfies the condition {overscore (p)}<

2^l.

33. A medical imaging system in accordance with claim 31 wherein to define an initial scatter estimation, said computer further configured to define an initial scatter estimation s⁽⁰⁾ in accordance with $s^{\left(0\right)}=\frac{p*y}{1+\stackrel{\_}{p}}=\frac{p*\left(b+p*b\right)}{1+\stackrel{\_}{p}}=\frac{p*b*(\delta }{}$

+p)1+p_,

where;

δ

is the Kronecker delta function;

p is a scatter kernel;

{overscore (p)} is a scatter kernel norm; and

b is a direct image.

34. A medical imaging system in accordance with claim 31 wherein to define an initial direct estimation, said computer further configured to define an initial direct estimation in accordance with $b^{\left(n\right)}=\frac{b}{2^l}+\frac{p*b}{2^l}+(\frac{2^l-1}{2^l}$

 



δ

-p2l)*b(n-1),

where;

δ

is the Kronecker delta function;

p is a scatter kernel;

l is an integer that satisfies the condition {overscore (p)}<

2^l;

bⁿ is an estimate of the image formed by directly transmitted photons; and

n is a quantity of iterations.

35. A medical imaging system in accordance with claim 31 wherein to re-define a direct image, said computer further configured to re-define a direct image in accordance with b⁽⁰⁾=y−

s⁽⁰⁾,

where;

b is a direct image;

s is a scatter image; and

y is an image including the direct image and the scatter image.