Compressed Sensing Magnetic Resonance Imaging Algorithms And Implementation

Compressed Sensing theory is always at the forefront of research in recent years, it is a new information sampling theory, which through developing the sparse characteristic of signals. Its advantage is reflected in the amount of data of signal measured value is far less than the amount of data which is obtained by conventional Nyquist sampling. It has been widely used in information theory, medical magnetic resonance imaging processing, pattern recognition, wireless communications and other fields. And the compressed sensing sparse signal reconstruction is the core issue of compressed sensing theory research, especially being used in the medical magnetic resonance imaging field, because of the presence of noise and artifacts, the reconstruction quality of magnetic resonance imaging is limited, while the compressive sensing theory can solve this problem well. So compressed sensing magnetic resonance imaging algorithms have certain theoretical significance and practical value.First, the application background and fundamental knowledge of compressed sensing theory are introduced by the thesis, the basic principle of magnetic resonance imaging is explained. According to the deficiency of magnetic resonance imaging, imaging methods to combine the theory of compressed sensing is presented.Then, three typical reconstruction algorithms which are applicated in the magnetic resonance imaging field are analysised: traditional Gradient Projection Sparse Reconstruction(GPSR) method?Two-step Iterative Shrinkage/Thresholding(TWIST) method and Reconstruction from Partial Fourier(Rec PF) algorithm. GPSR is a representative algorithm of the traditional reconstruction algorithms, because of the poor reconstruction quality, and there is too much noise in local area, so TWIST method which combined with Total Variation(TV) model the paper is analysised, there are noise still in local area of reconstruction result and can not reconstruct image accurately, aiming at the problem, Rec PF algorithm is analysised again, it regards Alternative Direction Method(ADM) as the core. Based on these algorithms, in order to improving reconstruction quality, Total Generalized Variation(TGV) model is drew into Alternating Direction Multiplier Method(ADMM) algorithm by the thesis. We compare it with existing GPSR, TWIST and Rec PF algorithms and analysis them through stimulating. It proves that ADMM algorithm combined with TGV model is effective. It improves the reconstruction quality and peak signal to noise ratio of brain images and decreases relative error through simulating, for brain images of high resolution and rich detail, its texture and detail are more clearer. When sampling rate is decreasing, we compare the stimulate result of Rec PF with ADMM, it proves that ADMM algorithm has stronger robustness as sampling rate decreasing, it has relative steady reconstruction quality.Finally, to study and research further, the basic function of graphical user interface(GUI)is studied and relative GUI is designed according to algorithms of the thesis. It realizes the basic function and intuitionistic compare of the related algorithms. From the view of user experience, GUI design achieves aesthetic and humane, reflects its convenience and applicability.