Magnetic resonance method and tomography system for acquiring image data sets

1. A method for acquiring magnetic resonance (MR) image data, comprising:

operating an MR data acquisition device to acquire at least two temporally separate raw data sets, each representing a plurality of pixels, with one phase measurement value being acquired for each pixel in each raw image data set;

providing said raw image data sets to a processor and, in said processor, executing an optimization algorithm for shared calculation of corrected phase values for the pixels in the respective raw image data sets, with corrected phase values for the pixels in a first of the raw image data sets, for each pixel, being dependent on at least one the phase measurement value of the respective pixel at a same location in a second of the raw image data sets acquired before or after said first of said raw image data sets, and with corrected phase values of the respective pixels in the second of the raw image data sets, for each pixel, being dependent on at least one the phase measurement value of the pixel at the same location in said first of said raw image data sets;

executing said optimization algorithm with an algorithm constraint that corrected phase values of all pixels in said first of said raw image data sets are identical to the phase measurement values of said pixels; and

in said processor, generating corrected image data sets from the corrected phase values, and making the corrected image data sets available in electronic form at an output of said processor.

2. The method as claimed in claim 1 comprising, in said optimization algorithm:

determining a plurality of first pairs of pixels, wherein each first pair of pixels consists of a first and a second pixel in one of the original data sets, the first pixel and the second pixel being adjacent,

determining a plurality of second pairs of pixels, wherein each second pair of pixels consists of a first pixel in one of the original data sets and of a second pixel in another of the original data sets which map the same location, the original data set and the other original data set being recorded temporally consecutively;

determining an error value variable for each pair of pixels, said error value variable depending on the phase measured values and the corrected phase values of the pixels in the pair of pixels;

determining a cost function as a weighted p-norm of the error value variables of the pairs of pixels; and

determining the corrected phase values by minimizing the cost function.

3. The method as claimed in claim 2 comprising determining said error value variable by:

calculating a measured phase difference by applying a modulo operation to the difference between the phase measured values of the first and of the second pixel in the pair of pixels, wherein an offset is added in particular before applying the modulo operation and the same offset is subtracted after the offset operation;

determining a corrected phase difference by subtracting the corrected phases of the first and of the second pixel in the pair of pixels; and

determining the error value variable by subtracting the measured phase difference from the corrected phase difference.

4. The method as claimed in claim 3 comprising calculating said measured phase difference between ±180° regardless of the phase values of the pixels for which said phase difference is calculated.

5. The method as claimed in claim 2 comprising minimizing said cost function using an iterative technique for solving linear equation systems.

6. The method as claimed in claim 5 comprising using, as said iterative technique, a preconditioned technique of conjugated gradients with a preconditioning matrix.

7. The method as claimed in claim 6 comprising determining said preconditioning matrix by solving an unweighted minimization problem.

8. The method as claimed in claim 7 comprising solving said unweighted minimization problem under a constraint that corrected phase values of all pixels said first of said raw image data sets are identical to phase measurement values of said pixels.

9. The method as claimed in claim 6 comprising, in said preconditioned technique of conjugated gradients, calculating an inverse of said preconditioning matrix using a Cholesky decomposition.

10. The method as claimed in claim 9 comprising using a two-norm as said p-norm.

11. The method as claimed in claim 2 comprising using a two-norm as said p-norm.

12. The method as claimed in claim 1 comprising, for each pixel in each raw image data set, forming at least one pair of pixels that includes the respective pixel.

13. The method as claimed in claim 1 comprising acquiring said raw image data sets as two-dimensional raw image data sets.

14. A magnetic resonance (MR) tomography apparatus comprising:

an MR data acquisition unit;

a processor configured to operate the MR data acquisition device to acquire at least two temporally separate raw data sets, each representing a plurality of pixels, with one phase measurement value being acquired for each pixel in each raw image data set;

said processor being provided with said raw image data sets to a processor, said processor being configured to execute an optimization algorithm for shared calculation of corrected phase values for the pixels in the respective raw image data sets, with corrected phase values for the pixels in a first of the raw image data sets, for each pixel, being dependent on at least one the phase measurement value of the respective pixel at a same location in a second of the raw image data sets acquired before or after said first of said raw image data sets, and with corrected phase values of the respective pixels in the second of the raw image data sets, for each pixel, being dependent on at least one the phase measurement value of the pixel at the same location in said first of said raw image data sets;

said processor being configured to execute said optimization algorithm with an algorithm constraint that corrected phase values of all pixels in said first of said raw image data sets are identical to the phase measurement values of said pixels; and

said processor being configured to generate corrected image data sets from the corrected phase values, and to make the corrected image data sets available in electronic form at an output of said processor.