Rapid Dynamic Magnetic Resonance Imaging Based On Compressed Sensing

The conventional Nyquist sampling theory requires the sampling frequency must be at least twice the highest frequency of signal, but in many cases it doesn’t achieve the requirement, because of the large signal bandwidth. Recently Donoho and Candes have proposed compressed sensing theory, which solves sparse regularization problem using nonlinear optimum algorithm and thus greatly reducing the measurement needed for reconstruction. At present the study of CS is still in the first stage, and most of studies are about the basic theory and the recovery of one dimensional signal. Aiming at accelerating signal recovering speed and improving recovered quality, we apply compressed sensing to the dynamic MRI image reconstruction based on in-depth study of existing methods. The following aspects are mainly investigated in this paper:The classical k-t FOCUSS algorithm is studied, and a method based FISTA algorithm is proposed for dynamic MRI imaging. With the penalty of x-f field’s sparsity, total variation and low rank structure respectly, the proposed method is applied to dynamic MRI imaging. Experiments show that the method has good convergence speed and good reconstruction result.Aiming at solving compound regularization problem, we propose a method based fast composite splitting algorithm for dynamic MRI imaging. The proposed method can combine multiple prior information, so we apply this method to dynamic MRI imaging, first with the combination of x-f field’s sparsity and low rank structure, then with the combination of total variation’s sparsity and low rank structure. Experiments show that the proposed method is better than the conventional single regularization problem and we can get better reconstruction result with the appropriate regularization combination.We propose a dynamic MRI imaging method based Bregman algorithm and alternate minimization algorithm. The Bregman algorithm can accelerate the convergence speed of alternate minimization algorithm, thus reducing the dependence on the continuation parameters and it can also deal with the noncovex penalty. We apply this method to dynamic MRI imaging, first with the combination of x-f field’s sparsity and low rank structure, then with the combination of total variation’s sparsity and low rank structure. Experiments show that the propose algorithm can get good reconstruction result within shorter time than the original alternate minimization algorith.