Method and magnetic resonance apparatus to determine a magnetic resonance image from magnetic resonance data

1. A method to generate a magnetic resonance image from magnetic resonance data entered into k-space in a data acquisition procedure executed by a magnetic resonance apparatus in which a basic magnetic field is present in an imaging region from which the magnetic resonance data were acquired, the basic magnetic field deviating from ideal homogeneity in the imaging region by a deviation described by an interference field, and wherein the magnetic resonance data entered into k-space are acquired along a readout direction defined by a read out gradient generated in the magnetic resonance apparatus, said method comprising:

in a computer having access to said data entered into k-space, calculating a transformation matrix dependent on said interference field and generating an inverse transformation matrix that is the inverse of said transformation matrix;

in said computer, transforming said magnetic resonance data entered into k-space into the image domain, as image data, by multiplying at least said magnetic resonance data entered into k-space along said readout direction by said inverse transformation matrix; and

making said image data available in electronic form at an output of said computer, in a format allowing display of an image represented by said image data.

2. A method as claimed in claim 1 comprising, in said computer, calculating said transformation matrix dependent on said interference field based on a Fourier transformation of said magnetic resonance data from a measured spin density distribution, without said interference field, and discretization of the image domain and k-space.

3. A method as claimed in claim 1 comprising implementing said Fourier transformation in said computer in directions that were not used to calculate said transformation matrix.

4. A method as claimed in claim 1 comprising generating a transformation matrix for each spatial direction in the image domain.

5. A method as claimed in claim 1 comprising determining said interference field by implementing a B0 measurement of said basic magnetic field.

6. A method as claimed in claim 1 comprising, in said computer, supplementing said transformation matrix with a selection function before multiplying said data in k-space with said transformation matrix, said selection function describing an excitation of nuclear spins at different locations in said imaging region, determined from a spectrum of an excitation pulse used to excite said spins in said procedure, and said interference field.

7. A method as claimed in claim 6 comprising employing a selection function that has a value of 0 for all spins that are not defined by said excitation pulse.

8. A method as claimed in claim 6 comprising using a selection function formed by at least one heavy side Heaviside function using a spectral width of an excitation pulse used to excite nuclear spins in said procedure.

9. A method as claimed in claim 6 comprising forming said selection function to describe an excitation strength of nuclear spins at different locations.

10. A method as claimed in claim 9 comprising normalizing said excitation strength to values between 0 and 1.

11. A magnetic resonance apparatus comprising:

a magnetic resonance data acquisition unit in which a basic magnetic field is present in an imaging region, the basic magnetic field deviating from ideal homogeneity in the imaging region by a deviation described by an interference field;

a control unit configured to operate the magnetic resonance data acquisition unit to acquire magnetic resonance data from said imaging region according to a data acquisition procedure, and to enter the acquired magnetic resonance data into k-space along a readout direction defined by a read out gradient generated in the magnetic resonance data acquisition unit;

a computer having access to said data entered into k-space configured to calculate a transformation matrix dependent on said interference field and to generate an inverse transformation matrix that is the inverse of said transformation matrix;

said computer being configured to transform said magnetic resonance data entered into k-space into the image domain, as image data, by multiplying at least said magnetic resonance data entered into k-space along said readout direction by said inverse transformation matrix; and

said computer being configured to make said image data available in electronic form at an output of said computer, in a format allowing display of an image represented by said image data.

12. A non-transitory, computer-readable data storage medium encoded with programming instructions said storage medium being loaded into a computer of a magnetic resonance apparatus in which a basic magnetic field is present in an imaging region, the basic magnetic field deviating from ideal homogeneity in the imaging region by a deviation described by an interference field, said programming instructions causing said computer to:

operate the magnetic resonance apparatus to acquire magnetic data from the imaging region in a data acquisition procedure, and to enter the acquired magnetic resonance data entered into k-space are acquired along a readout direction defined by a read out gradient generated in the magnetic resonance apparatus;

calculate a transformation matrix dependent on said interference field and generate an inverse transformation matrix that is the inverse of said transformation matrix;

transform said magnetic resonance data entered into k-space into the image domain, as image data, by multiplying at least said MR data entered into k-space along said readout direction by said inverse transformation matrix; and

make said image data available in electronic form at an output of said computer, in a format allowing display of an image represented by said image data.