Reconstruction of MRI Data Using Sparse Matrix Inverses

In this paper, we propose a method for reconstruction of MR images from k-space data sampled on non-Cartesian trajectories. We approach the problem approximating the full matrix pseudoinverse by a sparse matrix. We find the optimal sparsity pattern by minimizing the approximation error using an efficient recursive algorithm. The new method is demonstrated with simulated radial data. The optimized method outperforms a non-optimized sparse matrix inverse approach both in terms of reconstruction speed and storage requirements (by a factor of 2-5) while providing a similar level of reconstruction error. The new method also performs significantly better than a standard regridding approach in terms of computational speed, accuracy and storage.