Fast Multi-Coil Parallel MR Imaging Based on a Combination of the Optimum Interpolation Approximation and Compressed Sensing

This paper introduces a new parallel imaging method based on a combination of the optimum interpolation approximation (OIA) and compressed sensing (CS) method. The proposed method is a kind of improved SENSE method because all sensitivity maps of receiver coils are assumed to be known. Firstly, we introduce a theory of the OIA that minimizes the supremum value of any measure of approximation error. Secondly, a practical method of computing the optimum interpolation functions of the OIA is presented. Because the proof of the optimality is based on the set theory, the OIA is optimized for a group of MR images, not for particular ones. Thirdly, we present a new combinational method of the OIA and the CS method. In this method, the sufficiently accurate reconstruction of a particular target MR image by the CS method is used as the weighting function of the OIA. Because the accuracy of the OIA tends to improve as the weighting function approaches to the target MR image, the proposed combinational method becomes optimum for reconstructing the particular target MR image. Finally, we compare the reconstruction accuracy of the proposed combinational method with that of the CS-only method.