Reducing distortion in magnetic resonance images

1. A machine-implemented method for reducing image distortion in magnetic resonance imaging (MRI), comprising:

receiving a first MRI image and a second MRI image, wherein the first MRI image and the second MRI image were acquired using different gradient fields;

estimating displacements of voxels between the first MRI image and the second MRI image by minimizing a cost function expressing a cost of the displacements;

reducing distortion in an MRI image using the estimated displacements; and

making the MRI image having reduced distortion available.

2. The method of claim 1 , wherein estimating the displacements of the voxels comprises iteratively minimizing a collection of cost functions expressing costs of displacements of different versions of the first MRI image and the second MRI image, wherein the different versions have been smoothed to different extents.

3. The method of claim 1 , wherein estimating the displacements of the voxels comprises:

producing a Hessian of the cost function; and

perturbing the Hessian of the cost function around a current estimate of the displacements using sparse matrix techniques.

4. The method of claim 1 , wherein estimating the displacements of the voxels comprises minimizing

F

⁡

(

u

1

,

…

⁢

,

u

N

)

=

1

N

⁢

∑

i

=

1

N

⁢

[

J

1

⁢

i

⁢

I

1

⁡

(

r

→

+

u

i

⁢

y

^

)

-

J

2

⁢

i

⁢

I

2

⁡

(

r

→

-

u

i

⁢

y

^

)

]

2

+

λ

1

⁢

∑

i

=

1

N

⁢

u

i

2

+

λ

2

⁢

∑

i

=

1

N

⁢

[

∇

→

i

⁢

u

i

]

2

.

5. The method of claim 1 , wherein reducing the distortion in the MRI image comprises reducing the distortion in the first MRI image or in the second MRI image.

6. The method of claim 1 , wherein making the MRI image having reduced distortion available comprises physically transforming a display screen to display the MRI image having reduced distortion or physically transforming a memory element in a data storage device to store data describing the MRI image having reduced distortion.

7. The method of claim 1 , wherein the cost function comprises:

a data term that that reflects a match between predicted and observed values of voxel coordinates; and

a regularization part that reflects the physical properties of a magnetic field.

8. An article comprising one or more non-transitory machine-readable media storing instructions operable to cause one or more machines to perform operations, the operations comprising:

estimating displacements of voxels between a forward gradient MRI image and a reverse gradient MRI image by finding an extremum of an expression that is a function of the displacements.

9. The article of claim 8 , finding the extremum comprises using sparse matrix techniques.

10. The article of claim 8 , wherein finding the extremum comprises perturbing a Hessian of a cost function that expresses a cost of the displacements of the voxels.

11. The article of claim 9 , wherein perturbing the Hessian of the cost function comprises perturbing the Hessian of quadratic approximation of the cost function.

12. The article of claim 8 , wherein estimating the displacements of the voxels comprises smoothing the forward gradient MRI image and the reverse gradient MRI image to reduce high spatial frequency content.

13. The article of claim 12 , wherein the expression comprises a function of the displacements of the voxels between the smoothed forward gradient MRI image and the smoothed reverse gradient MRI image.

14. The article of claim 12 , wherein the expression comprises:

H ( {right arrow over (u)} )· {right arrow over (v)}=−{right arrow over (g)} ( {right arrow over (u)} ),

where

H({right arrow over (u)}) is the Hessian of a cost function at {right arrow over (u)}, and

{right arrow over (g)}({right arrow over (u)}) is the gradient of the cost function at {right arrow over (u)}.

15. A machine-implemented method comprising:

smoothing MRI images to yield first smoothed MRI images;

expressing a cost of displacements of voxels in the first smoothed MRI images in a first expression;

perturbing the first expression to yield a first approximation of the displacements of the voxels;

smoothing the MRI images to yield second smoothed MRI images, wherein the second smoothed MRI images include higher spatial frequency content than the first smoothed MRI images;

expressing a cost of the displacements of voxels in the second smoothed MRI images in a second expression; and

perturbing the second expression about the first approximation to yield a second approximation of the displacements of the voxels.

16. A machine-implemented method for magnetic resonance imaging (MRI), comprising:

using data from acquired raw MRI images with opposite-gradient magnetic fields to construct a cost function for an MRI displacement field caused by applied magnetic fields in acquiring the raw MRI images, the cost function comprising: (1) a term involving the voxel-by-voxel difference of image intensities, which are scaled by the local dilation; (2) a term to keep the MRI displacement field smooth over the whole volume; and (3) a scale term for the MRI displacement field; and

minimizing the cost function to extract correct MRI displacement for each voxel.

17. The method of claim 16 , comprising:

using the MRI displacement field to construct an MRI image with reduced image distortions.

18. The method of claim 16 , wherein minimizing of the cost function comprises:

applying a convolution processing to smooth the images;

applying Newton's method to the cost function of the smoothed images to construct a matrix equation as the Hessian of the cost function; and

processing the matrix equation to find a solution for the MRI displacement field which corrects the distortions and aligns the images) at a current level of smoothing.

19. The method of claim 16 , further comprising:

iterating the minimizing of the cost function at different levels of smoothing to obtain the displacement field.

20. A magnetic resonance imaging system comprising:

a scanner configured to acquire a first MRI image and a second MRI image using different gradient fields; and

a data processing apparatus configured to:

receive the first MRI image and the second MRI image;

estimate displacements of voxels between the first MRI image and the second MRI image by minimizing a cost function expressing a cost of the displacements; and

reduce distortion in an MRI image using the estimated displacements.