Phase estimation for retrospective motion correction

A non-transitory computer readable medium having instructions stored thereon that, when executed by one or more processors of a magnetic resonance apparatus, cause the magnetic resonance apparatus to acquire clinical images of an object that is moving during at least a portion of a magnetic resonance imaging (MRI) scan by:

• generate, using a SENSitivity Encoding (SENSE) plus motion model reconstruction, an initial image of the object using k-space data and motion parameters that are acquired over a plurality of motion states of the object;
• perform a projection onto convex sets (POCS) reconstruction of the initial image to generate a plurality of projection images such that each respective one of the plurality of projection images is associated with a projection of the initial image onto each respective one of the plurality of motion states motion states;
• calculate a refined image from each one of the plurality of projection images using the SENSE plus motion model that further incorporates a calculated phase difference map for each motion state corresponding to each respective one of the plurality of projection images;
• iteratively repeat (i) performing the POCS reconstruction from refined images calculated in a previous iteration to calculate a plurality of projection images, and (ii) calculating a further refined image from the plurality of projection images until a data consistency error improvement of the SENSE plus motion model is less than a predetermined threshold value;
• and
• store a calculated refined image corresponding to an iteration in which the data consistency error improvement is less than the predetermined threshold value.