Toeplitz-Based Iterative Image Reconstruction for MRI With Correction for Magnetic Field Inhomogeneity

In some types of magnetic resonance (MR) imaging, particularly functional brain scans, the conventional Fourier model for the measurements is inaccurate. Magnetic field inhomogeneities, which are caused by imperfect main fields and by magnetic susceptibility variations, induce distortions in images that are reconstructed by conventional Fourier methods. These artifacts hamper the use of functional MR imaging (fMRI) in brain regions near air/tissue interfaces. Recently, iterative methods that combine the conjugate gradient (CG) algorithm with nonuniform FFT (NUFFT) operations have been shown to provide considerably improved image quality relative to the conjugate-phase method. However, for non-Cartesian k-space trajectories, each CG-NUFFT iteration requires numerous k-space interpolations; these are operations that are computationally expensive and poorly suited to fast hardware implementations. This paper proposes a faster iterative approach to field-corrected MR image reconstruction based on the CG algorithm and certain Toeplitz matrices. This CG-Toeplitz approach requires k-space interpolations only for the initial iteration; thereafter, only fast Fourier transforms (FFTs) are required. Simulation results show that the proposed CG-Toeplitz approach produces equivalent image quality as the CG-NUFFT method with significantly reduced computation time.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/85903/1/Fessler50.pd

Stochastic Optimization of 3D Non-Cartesian Sampling Trajectory (SNOPY)

Optimizing 3D k-space sampling trajectories for efficient MRI is important yet challenging. This work proposes a generalized framework for optimizing 3D non-Cartesian sampling patterns via data-driven optimization. We built a differentiable MRI system model to enable gradient-based methods for sampling trajectory optimization. By combining training losses, the algorithm can simultaneously optimize multiple properties of sampling patterns, including image quality, hardware constraints (maximum slew rate and gradient strength), reduced peripheral nerve stimulation (PNS), and parameter-weighted contrast. The proposed method can either optimize the gradient waveform (spline-based freeform optimization) or optimize properties of given sampling trajectories (such as the rotation angle of radial trajectories). Notably, the method optimizes sampling trajectories synergistically with either model-based or learning-based reconstruction methods. We proposed several strategies to alleviate the severe non-convexity and huge computation demand posed by the high-dimensional optimization. The corresponding code is organized as an open-source, easy-to-use toolbox. We applied the optimized trajectory to multiple applications including structural and functional imaging. In the simulation studies, the reconstruction PSNR of a 3D kooshball trajectory was increased by 4 dB with SNOPY optimization. In the prospective studies, by optimizing the rotation angles of a stack-of-stars (SOS) trajectory, SNOPY improved the PSNR by 1.4dB compared to the best empirical method. Optimizing the gradient waveform of a rotational EPI trajectory improved subjects' rating of the PNS effect from 'strong' to 'mild.' In short, SNOPY provides an efficient data-driven and optimization-based method to tailor non-Cartesian sampling trajectories.Comment: 13 pages, 8 figure