Method and apparatus for field map estimation

1. A method for estimating values of a field map in a magnetic resonance (MR) imaging system, the method comprising:

a) applying a magnetic resonance excitation;

b) acquiring a set of MR images at multiple echo times based on the magnetic resonance excitation;

c) determining a set of feasible field map values for a pixel in a field map from the set of MR images; and

d) estimating a value of the field map by choosing a field map value for the pixel from the set of feasible field map values using a combinatorial optimization algorithm that includes a smoothness constraint.

2. The method, as recited in claim 1 , wherein determining the set of feasible field map values for the pixel comprises:

i) calculating a cost function for the pixel from the acquired plurality of MR images;

ii) locating local minima of the cost function across a range of field inhomogeneity values; and

iii) determining the set of feasible field map values for the pixel from field inhomogeneity values at the local minima of the cost function.

3. The method, as recited in claim 2 , wherein the cost function is a least squares residue function.

4. The method, as recited in claim 1 , wherein the combinatorial optimization algorithm comprises:

i) for one or more iterations, communicating a set of sum-product belief messages between the pixel and one or more neighboring pixels of the pixel in the field map;

ii) calculating a belief vector for the pixel based on the set of sum-product belief messages received from the one or more neighboring pixels in each iteration; and

iii) choosing a most likely field map value from the set of feasible field map values using the belief vector after the one or more iterations.

5. The method, as recited in claim 4 , wherein a sum-product belief message in the set of sum-product belief messages comprises an estimated likelihood of a feasible field map value for the pixel.

6. The method, as recited in claim 4 , wherein an element of the belief vector comprises an overall likelihood of a feasible field map value for the pixel.

7. The method, as recited in claim 1 , wherein the combinatorial optimization algorithm comprises:

i) estimating a most likely field map value from the set of feasible field map values for the pixel in the field map; and

ii) fixing a field map value of the pixel to the estimated most likely field map value if the pixel satisfies the smoothness constraint with its neighboring pixels.

8. The method, as recited in claim 1 , wherein the combinatorial optimization algorithm comprises:

i) estimating a most likely field map value from the set of feasible field map values for the pixel in the field map; and

ii) fixing a field map value of the pixel by selecting a field map value from the set of feasible field map values, wherein the field map value selected is adjacent to the estimated most likely field map value if the pixel does not satisfy the smoothness constraint with its neighboring pixels.

9. The method, as recited in claim 1 , wherein the combinatorial optimization algorithm comprises minimizing a number of inconsistent pairs of field map values for neighboring pixels in the field map.

10. The method, as recited in claim 1 , wherein a number of chemical species separable by the field map is less than a cardinality of the set of MR images.

11. The method, as recited in claim 1 , further comprising using the estimated field map to generate a magnetic resonance display image with species separation.

12. A magnetic resonance imaging apparatus, comprising:

a magnetic resonance excitation and detection system; and

a controller electrically connected to the magnetic resonance imaging excitation and detection system, comprising:

a display;

at least one processor; and

computer readable media, comprising:

computer readable code for generating an estimated field map, comprising:

a) computer readable code for applying a magnetic resonance excitation;

b) computer readable code for acquiring a set of MR images at multiple echo times based on the magnetic resonance excitation;

c) computer readable code for determining a set of feasible field map values for a pixel in a field map from the set of MR images;

d) computer readable code for estimating a value of the field map by choosing a field map value for the pixel from the set of feasible field map values using a combinatorial optimization algorithm that includes a smoothness constraint;

computer readable code for generating a magnetic resonance display image with species separation using the estimated field map.

13. The apparatus, as recited in claim 12 , wherein the computer readable code for determining a set of feasible field map values for a pixel comprises:

computer readable code for calculating a cost function for the pixel from the acquired plurality of MR images;

computer readable code for locating local minima of the cost function across a range of field inhomogeneity values; and

computer readable code for determining the set of feasible field map values for the pixel from field inhomogeneity values at the local minima of the cost function.

14. The apparatus, as recited in claim 13 , wherein the cost function is a least squares residue function.

15. The apparatus, as recited in claim 12 , wherein the computer readable code for estimating a value of the field map using a combinatorial optimization algorithm comprises:

computer readable code for communicating a set of sum-product belief messages between the pixel and one or more neighboring pixels of the pixel in the field map for one or more iterations;

computer readable code for calculating a belief vector for the pixel based on the set of sum-product belief messages received from the one or more neighboring pixels in each iteration; and

computer readable code for choosing a most likely field map value from the set of feasible field map values using the belief vector after the one or more iterations.

16. The apparatus, as recited in claim 15 , wherein a sum-product belief message in the set of sum-product belief messages comprises an estimated likelihood of a feasible field map value for the pixel.

17. The apparatus, as recited in claim 15 , wherein an element of the belief vector comprises an overall likelihood of a feasible field map value for the pixel.

18. The apparatus, as recited in claim 12 , wherein the computer readable code for estimating a value of the field map using a combinatorial optimization algorithm comprises:

computer readable code for estimating a most likely field map value from the set of feasible field map values for the pixel in the field map; and

computer readable code for fixing a field map value of the pixel to the estimated most likely field map value if the pixel satisfies the smoothness constraint with its neighboring pixels.

19. The apparatus, as recited in claim 12 , wherein the computer readable code for estimating a value of the field map using a combinatorial optimization algorithm comprises:

computer readable code for estimating a most likely field map value from the set of

feasible field map values for the pixel in the field map; and

computer readable code for fixing a field map value of the pixel to a field map value adjacent to the estimated most likely field map value if the pixel does not satisfy the smoothness constraint with its neighboring pixels.

20. The apparatus, as recited in claim 12 , wherein the computer readable code for estimating a value of the field map using a combinatorial optimization algorithm comprises:

computer readable code for minimizing a number of inconsistent pairs of field map values for neighboring pixels in the field map.