Patent ID: 8379951

Claim:
A method for obtaining an image by parallel acquisition magnetic resonance imaging (MRI), comprising: a) exciting precessing nuclear spins in a region of a subject; b) simultaneously obtaining a plurality of response signals, representing magnetic resonance signals arising from the precessing nuclear spins, from the region respectively with a plurality of RF reception coils, with each response signal representing a reduced data set of a totality of all of said response signals, wherein the reduced data set is a reduced k-space data set, and wherein the complete data set is a complete k-space data set; c) additionally obtaining calibration data points for each data set; d) synthesizing a filter using the calibration data points, wherein the synthesizing filter, comprises: selecting a data point of the calibration data points; and using data points adjacent to the selected data point to calculate the synthesizing filter, wherein the using the data points adjacent to the selected data point uses all data points adjacent to the selected data point to calculate the synthesizing filter for the selected data point, wherein the synthesizing filter is sampling pattern independent and wherein the synthesizing filter provides calibration weights; e) applying the synthesizing filter to the reduced data set to obtain a plurality of coupled simultaneous linear equations with a plurality of unknowns, wherein the applying the synthesizing filter to the reduced k-space data set, comprises: selecting points; and applying the synthesizing filter, wherein for at least one of the selected points there is at least two of the combination of adjacent points used by the synthesizing filter and the selected point have unknown values; and f) solving the plurality of coupled simultaneously linear equations with the plurality of unknowns to obtain a complete data set, wherein the solving the plurality of simultaneous linear equations solves a constrained optimization, wherein the constrained optimization comprises minimizing |Gx−x| 2 and |Dx−y| 2 <ε, where x=[x 1 , x 2 , . . . , x n ] T is a desired full-grid multi-coil reconstructed k-space images, y=[y 1 , y 2 , . . . , y n ] T is the reduced k-space data set, G is the synthesizing filter, and D is a resampling operator and ε error less than noise.