A set of image-space data is reconstructed from a set of k-space data. The set of image-space data is generated by minimizing a cost functional by an iterative non-linear conjugate gradient process. The iterative process may be accelerated by introducing k-space weighting to the cost functional. With proper choice of k-space weighting, a block-Toeplitz matrix is generated which permits use of Fast Fourier Transform techniques. An image is rendered from the set of image-space data.