Iterative reconstruction of gradient echo Magnetic Resonance Images

A computer program comprising machine executable instructions for execution by a processor controlling a medical system, wherein execution of the machine executable instructions causes the processor to:

• receive measured gradient echo k-space data;
• receive an off-resonance phase map;
• reconstruct an initial image from the measured gradient echo k-space data;
• calculate an upsampled phase map from the off-resonance phase map;
• calculate an upsampled image from the initial image;
• calculating a modulated image by modulating the upsampled image with the upsampled phase map;
• calculate a corrected image comprising iteratively:
• calculating updated k-space data by applying a data consistency algorithm to a k-space representation of the modulated image and the measured gradient echo k-space data;
• and
• calculating an updated image from the updated k-space data, wherein calculation of the updated image comprises demodulation by the upsampled phase map wherein calculating the updated image further comprises applying a smoothing algorithm, wherein the modulated image for further iteration results from the updated image.

A method of operating a medical system, wherein the method comprises,

• receiving measured gradient echo k-space data;
• receiving an off-resonance phase map;
• reconstructing an initial image from the measured gradient echo k-space data;
• calculating an upsampled phase map from the off-resonance phase map;
• calculating an upsampled image from the initial image;
• calculating a modulated image by modulating the upsampled image with the upsampled phase map;
• calculating a corrected image comprising iteratively:
• calculating updated k-space data by applying a data consistency algorithm to a k-space representation of the modulated image and the measured gradient echo k-space data;
• and
• calculating an updated image from the updated k-space data, wherein calculation of the updated image comprises demodulation by the upsampled phase map wherein calculating the updated image further comprises applying a smoothing algorithm, wherein the modulated image for further iteration results from the updated image.