A fast & accurate non-iterative algorithm for regularized non-Cartesian MRI

We introduce a novel algorithm for regularized reconstruction of non-Cartesian MRI data. The proposed non-iterative scheme closely approximates the Tikhonov regularized least squares method, but provides a significant speed up over standard implementation based on iterative conjugate gradient algorithm. This computational complexity of the proposed scheme is comparable to that of gridding. However, the proposed scheme is significantly more robust to undersampling and measurement noise. Numerical simulations clearly demonstrate the advantages of the proposed algorithm over traditional schemes. The proposed algorithm may be very useful in dynamic and functional MRI applications, where the fast reconstruction of several undersampled images is required.