A medical system (100, 300) comprising: a memory storing machine executable instructions; a processor configured for controlling the medical system, wherein execution of the machine executable instructions causes the processor to: receive measured gradient echo k-space data from a magnetic resonance imaging system; receive an off-resonance phase map from the magnetic resonance imaging system; reconstruct an initial magnetization image from the measured gradient echo k-space data; calculate a modulated image; 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 calculating the updated image comprises applying a smoothing algorithm, wherein the modulated image for further iteration results from the updated image; characterized in that execution of the machine executable instructions further causes the processor to: calculate an upsampled phase map from the off-resonance phase map; calculate an upsampled image from the initial magnetization image, with same chosen resolution of the upsampled image and the upsampled phase map; wherein calculating the modulated image is performed by modulating the upsampled image with the upsampled phase map; wherein calculating the updated image further comprises demodulation by the upsampled phase map. a memory storing machine executable instructions; a processor configured for controlling the medical system, wherein execution of the machine executable instructions causes the processor to: receive measured gradient echo k-space data from a magnetic resonance imaging system; receive an off-resonance phase map from the magnetic resonance imaging system; reconstruct an initial magnetization image from the measured gradient echo k-space data; calculate a modulated image; 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 calculating the updated image comprises applying a smoothing algorithm, wherein the modulated image for further iteration results from the updated image; characterized in that execution of the machine executable instructions further causes the processor to: calculate an upsampled phase map from the off-resonance phase map; calculate an upsampled image from the initial magnetization image, with same chosen resolution of the upsampled image and the upsampled phase map; receive measured gradient echo k-space data from a magnetic resonance imaging system; receive an off-resonance phase map from the magnetic resonance imaging system; reconstruct an initial magnetization image from the measured gradient echo k-space data; calculate a modulated image; 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 calculating the updated image comprises applying a smoothing algorithm, wherein the modulated image for further iteration results from the updated image; characterized in that execution of the machine executable instructions further causes the processor to: 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 calculating the updated image comprises applying a smoothing algorithm, wherein the modulated image for further iteration results from the updated image; characterized in that execution of the machine executable instructions further causes the processor to: calculate an upsampled phase map from the off-resonance phase map; calculate an upsampled image from the initial magnetization image, with same chosen resolution of the upsampled image and the upsampled phase map; wherein calculating the modulated image is performed by modulating the upsampled image with the upsampled phase map; wherein calculating the updated image further comprises demodulation by the upsampled phase map.