Method for reconstructing a motion-corrected magnetic resonance image of a subject

A non-transitory computer readable storage medium comprising a set of computer-readable instructions stored thereon for reconstructing a motion-corrected magnetic resonance image of a subject, the computer-readable instructions that, when executed by at least one processor cause the at least one processor to:

• receive k-space magnetic resonance image data acquired of the subject using a multi-channel coil array during a magnetic resonance imaging acquisition;
• receive coil sensitivity maps of the multi-channel coil array;
• receive a motion trajectory comprising a series of motion states that were held by the subject during the acquisition;
• determine similarities across the motion states;
• form groups of motion states such that each group contains motion states that are similar to each other;
• and
• determine a single group motion state representing each group;
• compute, for each group of motion states, a single transformation operator and building a group-specific NuFT forward model, in which a mismatch between the coil sensitivity maps and the magnetic resonance image caused by a motion of the subject during the acquisition is reduced by operating the transformation operator on the coil sensitivity maps and/or on the magnetic resonance image;
• and
• reconstruct the motion-corrected magnetic resonance image by minimizing a data consistency error between the received k-space data and the group-specific NuFT forward models, wherein each NuFT forward model comprises an image estimate, the coil sensitivity maps, a non-uniform Fourier Transformation, and a phase factor corresponding to the motion state held by the subject at a time of acquiring the corresponding subset of k-space data.

A magnetic resonance apparatus comprising:

• a MR data acquisition scanner configured to acquire k-space magnetic resonance image data of a subject using a multi-channel coil array during a magnetic resonance imaging acquisition;
• and
• a data processing device configured to:
• receive coil sensitivity maps of the multi-channel coil array;
• receive a motion trajectory comprising a series of motion states that were held by the subject during the acquisition;
• determine similarities across the motion states;
• form groups of motion states such that each group contains motion states that are similar to each other;
• and
• determine a single group motion state representing each group;
• compute, for each group of motion states, a single transformation operator and building a group-specific NuFT forward model, in which a mismatch between the coil sensitivity maps and the magnetic resonance image caused by a motion of the subject during the acquisition is reduced by operating the transformation operator on the coil sensitivity maps and/or on the magnetic resonance image;
• and
• reconstruct the motion-corrected magnetic resonance image by minimizing a data consistency error between the received k-space data and the group-specific NuFT forward models, wherein each NuFT forward model comprises an image estimate, the coil sensitivity maps, a non-uniform Fourier Transformation, and a phase factor corresponding to the motion state held by the subject at a time of acquiring the corresponding subset of k-space data.