Research On Fast Magnetic Resonance Imaging Algorithm For Non-Cartesian Sampling Data

MRI can produce images of structure and function of internal tissues in living body noninvasively. Compared with others imaging modalities(such as CT), MRI has advantages of multi-parameters imaging and having no ionizing radiation, so it has been widely used in clinics and become an important diagnostic tool in medicine.The long data acquisition time can restrict the applications of MRI in clinics; so much work has been done to seek fast imaging methods, and non-Cartesian scanning methods are kind of them. Because of their insensitive to flow and fast data acquisition, non-Cartesian scanning methods are widely applied in areas such cardiac coronary artery imaging and functional brain imaging. As non-Cartesian sampling data do not distribute on equal spaced grid points, we can't reconstruct them by FFT directly, the usual way is to interpolate the non-Cartesian K-space data onto 2D Cartesian grid firstly, and then perform FFT to get the image, such as gridding, Non-uniform Fast Fourier Transform (NUFFT). However, the radial or spiral scanning usually samples high frequency data in K-space with low sampling density, which results in large approximation error on the grid points far away from measured data in high frequency domain when interpolation methods are applied. The feasible methods may be iterative reconstruction methods with prior constraints. The regularization functional is the key to restricting noise and artifacts efficiently during iteration. As classical L2 norms tend to reconstruct images with blurred edges, some authors choose L1 norm, total variation (TV), as the regularization functional, which can restrict artifacts and noise efficiently without smoothing sharp discontinuities. Therefore, our work mainly focuses on iterative reconstruction algorithm with TV functional for non-Cartesian MRI data in the article.Sparse MRI is a method which reduces data acquisition time by undersampling K-space data. If K space data is undersampled, the measured data do not meet the sampling theory any more, and images reconstructed from them by FFT suffer from severe artifacts. However, sparse MRI theory shows that if the sparse sampling in k-space is random and artifacts caused by it appear as noise in some transform domain such as wavelet transform and the desired image is sparse in that transform domain, we can also reconstruct the image accurately by an appropriate nonlinear reconstruction algorithm. As the speed of sparse MRI algorithm is slow, improving the speed of reconstruction algorithm may be a research fact of sparse MRI.The work we do on the reconstruction algorithms of non-Cartesian MRI data and sparse MRI data is as follows:(1) For non-Cartesian MR data reconstruction, an iterative algorithm based on POCS and TV minimization was proposed, which can be considered as an improved version of the constrained TV (CTV) minimization algorithm. This proposed algorithm redefines the data consistent constraint: it interpolates non-Cartesian data onto 2D Cartesian grid first, and then in the iterative process of TV minimization, the Fourier values on grid points close to measured data are replaced with the interpolated ones according to POCS principle, which imposes the data consistency of constraint. Experiments results show that the proposed algorithm can reconstruct images more accurately and rapidly than CTV algorithm.(2)The principle of the mentioned method above is introduced into sparse MRI. The improved method only regards the regularization functional as the objective function, which avoids the computation of system matrix. The experiments results show that the improved method reduces the amount of computation and increases the speed of reconstruction while ensuring the images' quality.