Research On Fast And Accurate Reconstruction For Radial And Propeller MRI Using The CTA-DFT Algorithm

Magnetic Resonance Imaging (MRI) is an important imaging modality based on Nuclear Magnetic Resonance (NMR). Compared with other modalities of medical imaging, such as X-ray, Computer Tomography(CT) and ultrasound, MRI has many advantages, such as with no ionizing radiation, imaging with multiple parameters in arbitrary plane, and providing excellent soft-tissue contrast. All those advantages make MR a very important tool for both research and clinical applications.The uniform K-space sampling of MRI, also called non-Cartesian K-space sampling, such as spiral, radial, or PROPELLER, has been receiving much attention in MRI due to its advantage of rapid scanning, nature of oversampling near the k-space center and ability to compensate for motion. As the sampling points are not positioned on the uniform grids, the fast Fourier transform (FFT) can’t be implemented straightforwardly for image reconstruction. Discrete Fourier transform (DFT) through the direct summation, also known as the conjugate phase reconstruction in the MRI community, could reconstruct the MR image from the non-Cartesian data with high precision and is widely used as a reference in evaluating the accuracy of other reconstruction methods. However, the high computation complexity makes the DFT impractical for clinical applications. Many fast algorithms, therefore, have been proposed for the reconstruction of non-Cartesian data.Many proposed fast algorithm such as gridding, Block Uniform Resampling (BURS), Generalized fast Fourier transform (GFFT), always resample the non-Cartesian data onto resampled onto the uniform grids through interpolation or solution of linear systems. However, these published "FFT" algorithms for non-equispaced data do not strictly compute the DFT of nonequispaced data, but rather some approximation.In this paper, we focus on the fast implementation of the DFT for some specific non-Cartesian trajectories, such as the radial or PROPELLER sampling which consists of lines with equally-spaced points. For each of these trajectories, the total non-Cartesian data can be grouped into subsets containing data uniformly lying on a line and the DFT of each subset data is computed through CTA(chirp transform algorithm) algorithm methods. Compared with the traditional DFT algorithm on the CPU, for a2562image, the CTA-DFT algorithm achieves approximately20times the acceleration which was further increased to1000times with our GPU approach. This study shows promise for the use of accurate DFT for future clinical applications.