Abstract: Spiral magnetic resonance imaging (MRI) plays an important role in functional imaging, parallel imaging and dynamic imaging. Most of the traditional image reconstruction algorithms for spiral imaging are based on kernel functions which interpolate the k-space data acquired with spiral trajectories onto a uniform grid in Cartesian space. Non-uniform fast Fourier transform (NUFFT) and least square method could then be applied after gridding to reconstruct the images. With these algorithms, the results are dependent on the choice of kernel function, and reconstruction errors are unavoidable during the gridding process. In this study, a spatio-temporal transform (STT) matrix, representing the relation between the image and sampled k-space data, is introduced in l₁ norm to optimize the problem based on spatio-temporal transform and compressed sensing (CS). The k-space data, rather than the after-gridding data, are used as the fidelity term, such that the gridding errors can be avoided. In addition, parallel computing on GPU can be applied to reduce the computation time for the STT matrix, making the algorithm more efficient.

Key words: spatio-temporal transformation(STT), compressed sensing(CS), parallel computing, spiral MRI, Non-uniform fast Fourier transform(NUFFT)