Method and magnetic resonance apparatus for determination of radio-frequency pulses

1. A method for determining a radio-frequency (RF) pulse for emission by a plurality of RF transmitting coils of a coil array of a magnetic resonance apparatus, wherein emission of said RF pulse by said plurality of RF transmitting coils influences a transverse magnetization of an object situated in the magnetic resonance apparatus, in a specified spatial region of the object, said method comprising:

providing a plurality of operating parameters of said magnetic resonance apparatus to a computer;

in said computer, representing said spatial region as an original vector and approximating said original vector, as an approximated vector, by decomposing said original vector into a finite number of weighted basis functions of a decomposition algorithm employed to decompose said original vector, to produce said approximated vector with a length that is less than a length of said original vector;

in said computer, determining said radio-frequency pulse as a function of said operating parameters and said approximated vector; and

making the determined RF pulse available at an output of said computer in an electronic form allowing operation of said RF coils of said coil array to emit said RF pulse.

2. A method as claimed in claim 1 comprising in said computer, determining said finite number of weighted basis functions as a function of a criterion specified to said computer that describes at least one of am accuracy of the approximated vector to said original vector, and a quality of said influence of said transverse magnetization in the specified spatial region by time-parallel emission of said determined radio-frequency pulse by said RF coils of said coil array.

3. A method as claimed in claim 2 comprising determining said weighted basis functions of said decomposition algorithm by executing an algorithm in said computer that causes said approximated vector to be sparse, said algorithm being selected from the group consisting of a matching pursuit algorithm and a wavelet algorithm.

4. A method as claimed in claim 2 comprising storing respective weights of said weighted basis functions either in a matrix of basis functions or in said approximated vector.

5. A method as claimed in claim 2 comprising randomly distributing respective weights of said weighted basis functions in a matrix of basis functions and in said approximated vector.

6. A method as claimed in claim 2 comprising selecting said criterion from the group consisting of a number of said basis functions, and an error in approximation of said original vector represented as a ratio of said approximated vector to said original vector.

7. A method as claimed in claim 1 comprising employing, as said weighted basis functions, predetermined functions selected from the group of function types consisting of Harr, Symlets, Meyer, Daubechies, Coiflets, Gabor, and Fermi.

8. A method as claimed in claim 1 wherein said operating parameters form an original system matrix of said magnetic resonance apparatus, and comprising, in said computer:

approximating an approximated system matrix by decomposing said original system matrix into a finite number of further basis functions, to produce said approximated system matrix with a dimension that is less than a dimension of said original system matrix;

said further basis functions being a pseudo-inversion matrix corresponding to a matrix of said basis functions; and

determining said RF pulse also as a function of said approximated system matrix.

9. A method as claimed in claim 8 wherein said criterion is an error of said approximated system matrix represented as a ratio of said approximated system matrix to said original system matrix.

10. A method as claimed in claim 8 comprising approximating said approximated system matrix by:

determining said pseudo-inversion matrix of said matrix of said basis functions; and

applying said pseudo-inversion matrix to said original system matrix and thereby producing said approximated system matrix as a sparse matrix with a number of columns equal to a number of columns of said original system matrix and a number of rows of said approximated system matrix being less than a number of rows of said original system matrix.

11. A method as claimed in claim 8 comprising determining said RF pulse as a numerical solution of a linear equation system in which said approximated system matrix links a solution vector, that describes said RF pulse, with said spatial region represented as said approximated vector.

12. A method as claimed in claim 11 comprising obtaining said numerical solution using a technique selected from the group consisting of LU decomposition of said approximated system matrix, ILU decomposition of said approximated system matrix, Cholesky decomposition of said approximated system matrix, iterative solving techniques, and parallel computational techniques.

13. A method as claimed in claim 1 comprising selecting said operating parameters from the group consisting of a k-space trajectory in k-space along which magnetic resonance data are entered into k-space during emission of said radio-frequency pulse, a measured field map of a basic magnetic field that exists during emission of said RF pulse, and a measured RF field map in said selected region.

14. A magnetic resonance apparatus comprising:

a magnetic resonance data acquisition unit comprising a plurality of radio-frequency (RF) transmitting coils in a coil array;

a control computer configured to operate said coil array to cause time-parallel emission of an RF pulse by said plurality of RF transmitting coils, so as to influence a transfer magnetization in a specified spatial region of an object situated in said data acquisition unit;

said control computer being configured to receive a plurality of operating parameters for said magnetic resonance data acquisition unit;

said control computer being configured to represent said spatial region as an original vector and approximate said original vector, as an approximated vector, by decomposing said original vector into a finite number of weighted basis functions of a decomposition algorithm employed to decompose said original vector, to produce said approximated vector with a length that is less than a length of said original vector;

said control computer being configured to determine said radio-frequency pulse as a function of said operating parameters and said approximated vector; and

said control computer being configured to make the determined RF pulse available at an output of said control computer in an electronic form and to operate said RF coils of said coil array to emit said RF pulse.