Fast spiral Fourier transform for iterative MR image reconstruction

We present a fast and accurate discrete spiral Fourier transform and its inverse. The inverse solves the problem of reconstructing an image from MRI data acquired along a spiral k-space trajectory. First, we define the spiral FT and its adjoint. These discrete operators allow us to efficiently compute the inverse using fast-converging conjugate gradient methods. Next, we developed a fast approximate spiral FT using the pseudo-polar FFT, to enhance the computational performances and numerical accuracy of the algorithm. Preliminary results demonstrate that the proposed algorithm is more accurate than existing iterative methods that use similar interpolation and grid size.