System and method for detecting and correcting registration misalignment of MR perfusion images

1. A method of correcting registration misalignment in magnetic resonance perfusion images, the method comprising the steps of: receiving a time series of magnetic resonance images of an anatomical organ, each said image comprising a plurality of intensities defined on an N-dimensional domain of points; performing a first group-wise registration of all images in the time series of images, using a pair-wise registration as an initialization; detecting a misaligned image from said group-wise registration by analyzing a total variation of intensity differences between consecutive images; and correcting said misaligned image by optimizing a second group-wise energy function over registration parameters of said misaligned image, wherein correcting said misaligned image comprises finding a set of rigid registration parameters P i =[p ik ], k=1, . . . , 6, of said misaligned transformation T i that minimizes {E(P(P i ))|P n , n≠i} wherein P=[P 1 , P 2 , . . . , P N ] is the set of registration parameters for all the images from said first group-wise registration wherein Nis a total number of images, E(P(P i )) is said second group-wise energy function calculated for P with varying P i and fixing P n , with n≠i.

2. The method of claim 1 , wherein performing said first group-wise registration of all images comprises randomly selecting a proper subset of points from said domain of points, forming a quadratic variation cost function

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wherein M is the number of randomly selected points, x m is a randomly selected point, N is the number of images in said time series of images, I n is an image in said time series of images, and T n is a rigid registration transformation, and finding a set of rigid transformations T n that minimize E, wherein the transformations T n are initialized by the initial pair-wise registration of all images.

3. The method of claim 2 , wherein finding a set of rigid transformations T n that minimize E comprises iterating P i+1 =P i +δP wherein P i is a set of registration parameters P=[P 1 , P 2 , . . . , P N ], where P i ={p ik , k=1, . . . , 6} are the rigid registration parameters for the transform T i at iteration step i, wherein δP is defined by

( J Z T ( x ) J Z ( x )+λdiag( J Z T ( x ) J Z ( x )))δ P=−J Z T ( x ) Z ( x ),

wherein J Z (x) is the Jacobian matrix of function Z(x) over the registration parameters P, wherein Z nm (x)=I n (T n (x m ))−I n′ (T n′ (x m )), J Z T (x) is the transpose of J Z (x), and λ is a damping factor to reduce a size of a convergence step.

4. The method of claim 1 , wherein detecting a misaligned image comprises calculating a total intensity variation between each pair of consecutive images I n and I n

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calculating h i =F i −max(F i−1 , F i+2 ), wherein transformation T i associated with variation F i is a misalignment if h i >α·σ wherein σ is a standard deviation of the F n 's and α is a predefined constant.

5. The method of claim 4 , wherein α·σ adaptively determines a threshold for a peak height of F n .

6. The method of claim 1 , wherein said second group-wise energy function is different from the first group-wise energy function.

7. The method of claim 6 , wherein said second group-wise energy function is a voxel wise entropy function.

8. A method of correcting registration misalignment in magnetic resonance perfusion images, said method comprising the steps of:

receiving a time series of magnetic resonance images of an anatomical organ, each said image comprising a plurality of intensities defined on an N-dimensional domain of points;

performing an initial rigid registration of all images in said time series of images;

detecting a misaligned image from said group-wise registration by analyzing a total variation of intensity differences between consecutive images; and

correcting said misaligned image by finding a set of rigid registration parameters P i =[p ik ], k=1, . . . , 6, of said misaligned transformation T i that minimizes {E(P(P i ))|P n , n≠i} wherein P=[P 1 , P 2 , . . . , P N ] is the set of registration parameters for all the images from said initial registration wherein N is a total number of images, E(P(P i )) is a voxel-wise entropy calculated for P with varying P i and fixing P n .

9. The method of claim 8 , wherein performing an initial rigid registration of all images comprises performing a first group-wise registration of all images in the time series of images, using a pair-wise registration as an initialization.

10. A program storage device readable by a computer, tangibly embodying a program of instructions executable by the computer to perform the method steps for correcting registration misalignment in magnetic resonance perfusion images, said method comprising the steps of:

receiving a time series of magnetic resonance images of an anatomical organ, each said image comprising a plurality of intensities defined on an N-dimensional domain of points;

performing a first group-wise registration of all images in the time series of images, using a pair-wise registration as an initialization;

detecting a misaligned image from said group-wise registration by analyzing a total variation of intensity differences between consecutive images; and

correcting said misaligned image by optimizing a second group-wise energy function over registration parameters of said misaligned image, wherein correcting said misaligned image comprises finding a set of rigid registration parameters P i =[p ik ], k=1, . . . , 6, of said misaligned transformation T i that minimizes {E(P(P i ))|P n , n≠i} wherein P=[P 1 , P 2 , . . . , P N ] is the set of registration parameters for all the images from said first group-wise registration wherein N is a total number of images, E(P(P i )) is said second group-wise energy function calculated for P with varying P i and fixing P n , with n≠i.

11. The computer readable program storage device of claim 10 , wherein performing said first group-wise registration of all images comprises randomly selecting a proper subset of points from said domain of points, forming a quadratic variation cost function

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n

=

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m

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1

M

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where

n

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{

N

for

⁢

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n

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1

,

n

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otherwise

,

wherein M is the number of randomly selected points, x m is a randomly selected point, N is the number of images in said time series of images, I n is an image in said time series of images, and T n is a rigid registration transformation, and finding a set of rigid to transformations T n that minimize E, wherein the transformations T n are initialized by the initial pair-wise registration of all images.

12. The computer readable program storage device of claim 11 , wherein finding a set of rigid transformations T n that minimize E comprises iterating P i+1 =P i +δP wherein P i is a set of registration parameters P=[P 1 , P 2 , . . . , P N ], where P i ={p ik , k=1, . . . , 6} are the rigid registration parameters for the transform T i at iteration step i, wherein δP is defined by

( J Z T ( x ) J Z ( x )+λdiag( J Z T ( x ) J Z ( x )))δ P=−J Z T ( x ) Z ( x ),

wherein J Z (x) is the Jacobian matrix of function Z(x) over the registration parameters P, wherein Z nm (x)=I n (T n (x m ))−I n′ (T n′ (x m )), J Z T (x) is the transpose of J Z (x), and λ is a damping factor to reduce a size of a convergence step.

13. The computer readable program storage device of claim 10 , wherein detecting a misaligned image comprises calculating a total intensity variation F n between each pair of consecutive images and I n and I n′ ,

F

n

=

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n

=

1

N

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

I

n

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n

′

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(

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n

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x

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

,

wherein N is a total number of images,

n

′

=

{

N

for

⁢

⁢

n

=

1

,

n

-

1

,

otherwise

,

calculating h i =F i −max(F i−1 , F i+2 ), wherein transformation T i associated with variation F i is a misalignment if h i >α·σ wherein σ is a standard deviation of the F n 's and α is a predefined constant.

14. The computer readable program storage device of claim 13 , wherein α·σ adaptively determines a threshold for a peak height of F n .

15. The computer readable program storage device of claim 10 , wherein said second group-wise energy function is different from the first group-wise energy function.

16. The computer readable program storage device of claim 15 , wherein said second group-wise energy function is a voxel wise entropy function.