EIGEN-VECTOR APPROACH FOR COIL SENSITIVITY MAPS ESTIMATION

摘要

A method for estimating a coil sensitivity map for a magnetic resonance (MR) image includes providing a matrix A of sliding blocks of a 3D image of coil calibration data, calculating a left singular matrix V_∥ from a singular value decomposition of A corresponding to τ leading singular values, calculating P=V_∥V_∥^H, calculating a matrix S that is an inverse Fourier transform of a zero-padded matrix P, and solving M^Hc^r=(S^r)^Hc^r for c^r, where c^r is a vector of coil sensitivity maps for all coils at spatial location r, and; $$ M=\left(\left(\begin{array}{cccc}1& 1& \dots & 1\\ 0& 0& \dots & 0\\ \dots & \dots & & \dots \\ 0& 0& \dots & 0\end{array}\right)\left(\begin{array}{cccc}0& 0& \dots & 0\\ 1& 1& \dots & 1\\ \dots & \dots & & \dots \\ 0& 0& \dots & 0\end{array}\right)\dots \left(\begin{array}{cccc}0& 0& \dots & 0\\ 0& 0& \dots & 0\\ \dots & \dots & & \dots \\ 1& 1& \dots & 1\end{array}\right)\right).$$