Phase-contrast MR imaging with speed encoding

1. A method for phase contrast magnetic resonance (MR) imaging with speed encoding, comprising:

operating an MR data acquisition unit according to an MR data acquisition sequence wherein nuclear spins in an examination subject are excited, and MR signals are acquired therefrom in at least one time period, with raw data representing said MR signals being acquired in each time period for a plurality of MR images, with said plurality of MR images comprising a reference MR image with flow compensation and at least one MR image with speed encoding;

providing said raw data to an image reconstruction computer and, in said image reconstruction computer, determining a plurality of matrices for each time period of said at least one time period such that the sum of said plurality of matrices is characterized by a pixel matrix with a plurality of matrix elements comprising matrix elements that represent pixel values for said reference MR image and other matrix elements representing pixel values for said at least one MR image with speed encoding, and such that a first matrix among said plurality of matrices fulfilling a predetermined first condition;

using said plurality of matrices to reconstruct an image of the examination subject; and

making said image of the examination subject available in electronic form at an output of said image reconstruction computer.

2. A method as claimed in claim 1 wherein said first condition is that signal contributions are suppressed in said first matrix that vary as at least one of a function of time or a function of said speed encoding.

3. A method as claimed in claim 1 wherein said first condition is dependent on an order of said first matrix.

4. A method as claimed in claim 3 wherein said first condition is that said order of said first matrix is less than a threshold value.

5. A method as claimed in claim 1 comprising determining the matrix elements of the respective matrices in said plurality of matrices by:

determining matrix elements of said first matrix;

determining matrix elements of a second matrix of said plurality of matrices; and

forming said pixel matrix as a sum of said first matrix and said second matrix.

6. A method as claimed in claim 5 comprising determining said matrix elements of said second matrix such that said second matrix fulfills a predetermined second condition that differs from said predetermined first condition.

7. A method as claimed in claim 6 wherein said second condition is that said second matrix contains matrix elements representing raw data originating from flowing nuclear spins in said subject.

8. A method as claimed in claim 6 wherein said second condition is a requirement that said second matrix be transformable into a matrix populated with matrix elements having a population density that is below a threshold value.

9. A method as claimed in claim 5 comprising determining the matrix elements of said first matrix and the matrix elements of said second matrix by minimizing a target function, said target function comprising at least one first regularization term that is dependent on the matrix elements of the first matrix and at least one second regularization term that is dependent on matrix elements of said second matrix.

10. A method as claimed in claim 9 wherein said first regularization term is independent of the matrix elements of the second matrix, and wherein said at least one second regularization term is independent of the matrix elements of the first matrix.

11. A method as claimed in claim 9 wherein said first regularization term is dependent on a nuclear norm for said first matrix.

12. A method as claimed in claim 9 wherein said at least one second regularization term comprises at least one of total variation and a focalized variation of matrix elements of said second matrix.

13. A method as claimed in claim 9 wherein the matrix elements of the first matrix and the matrix elements of the second matrix are determined collectively in an iterative procedure.

14. A method as claimed in claim 1 comprising, from said pixel matrix, automatically determining speed data for said flowing nuclear spins in said time periods.

15. A method as claimed in claim 1 comprising detecting said MR signals for acquiring said raw data by entering the raw data into a memory organized as k-space, with said raw data not completely filling k-space.

16. A magnetic resonance (MR) apparatus for phase contrast magnetic resonance imaging with speed encoding, comprising:

an MR data acquisition unit;

a control computer configured to operate an MR data acquisition unit according to an MR data acquisition sequence wherein nuclear spins in an examination subject are excited, and MR signals are acquired therefrom in at least one time period, with raw data representing said MR signals being acquired in each time period for a plurality of MR images, with said plurality of MR images comprising a reference MR image with flow compensation and at least one MR image with speed encoding;

an image reconstruction computer provided with said raw data, said image reconstruction computer being configured to determine a plurality of matrices for each time period of said at least one time period such that the sum of said plurality of matrices is characterized by a pixel matrix with a plurality of matrix elements comprising matrix elements that represent pixel values for said reference MR image and other matrix elements representing pixel values for said at least one MR image with speed encoding, and such that a first matrix among said plurality of matrices fulfilling a predetermined first condition;

said image reconstruction computer being configured to reconstruct an image of the examination subject using said plurality of matrices; and

said image reconstruction computer being configured to make said an image of the examination subject available in electronic form at an output of said image reconstruction computer.