Fast Simulator for Undersampling Artifact

          In optimization problems for MRF, artifacts from actual scans have to be considered.  However, simulating undersampling artifacts is rarely introduced in MRF optimization routines, mainly due to the following reasons: 1) the aliasing artifacts are spatially dependent, tissue compositions and spatial distribution need to be considered; 2) As compared to the implicative cost functions that measure signal magnitude and/or orthogonality, a more tractable approach is to directly minimize the errors of the resulting quantitative maps of tissue properties. However, error estimation need both image reconstruction and quantitative mapping, that in turn requires nonuniform Fourier transform (NUFFT) with additional steps of gridding and density compensation; these steps take the majority of the computational time. Specifically, the cost functions of a great amount of sequence candidates have to be evaluated to approach the optimal solution, and the artifacts from hundreds of images need to be computed in each sequence candidate. Around 44,000 iterations are performed from our example of using simulated annealing (SA) for MRF optimization (the maximum iterations in the SA algorithm are typically greater than 100, more complex objective functions require larger amounts of iterations of searching). Repeating the NUFFT and gridding calculations at each iteration in such optimization problem is therefore computationally expensive and impractical.

            We have been developing a fast image series simulator to address the computational challenge in MRF sequence optimization while providing simulated signals that best approximate the signals from actual in vivo scans with undersampling and system imperfections. The concept is similar to the partially separable models used in image reconstruction, where the time-resolved reconstructed images are represented as a product of low rank spatial and temporal basis functions.  Here, we use this concept to simulate aliased images of actual scans.