Research On Models And Fast Reconstruction Methods For MR Image Reconstruction

Magnetic resonance imaging is a non-invasive and non-radiative technique that al-lows visualization of structures and functions of a body. This technology has played an important role in early diagnosis of critical diseases with the advantages of multi-parameter, high-contrast and multidirectional imaging. However, slowing scanning speed (or long acquisition time) of magnetic resonance imaging, compared with oth-er imaging modalities, restricts its extensive application in clinic. The main reason is that, in the process of long time scan, the inadvertent movement of the scanned person maybe caused motion artifacts that blurs image content and results in the loss of impor-tant diagnostic information. Therefore, the research of fast imaging methods is a hot topic in magnetic resonance imaging field and has great value in theory research and clinic application.The conventional means that accelerate imaging by improving the rate of switching gradient field and hardware performance, such as the method with high-speed scanning sequence and the parallel acquisition method with multi-channel coils, have developed their limits as the restriction of physical, biological and hardware conditions. By con-sidering the directly proportional relationship between the quantity of samples and scan time, the acceleration methods by reducing the amount of data have become the focus of research field of fast magnetic resonance imaging.Magnetic resonance image reconstruction is a process of converting digital signal to image and is the main procedure of magnetic resonance imaging. The reconstruction can be described as an mathematical inverse problem. By using mathematical mean-s, modeling and designing optimal algorithms for this problem can achieve the goal to improve imaging speed of system. Generally, image reconstruction with partial data is an ill-posed inverse problem. Direct reconstruction can accelerate imaging, but can not obtain high quality image that meets the requirements of the clinical diagnosis. The emergence of compressed sensing theory effectively solves the reconstructed difficul-ty and provides a new framework for research of fast imaging methods. Compressed sensing-based magnetic resonance imaging methods indicate that, if the implicit spar-sity of images as prior knowledge is embedded in the foregoing ill-posed problem, we can reconstruct satisfying image by using less signal data. All research contents of this dissertation are established under the framework of compressed sensing-based recon-struction methods.By combining the projection operator and proximal-point method, this disserta- tion proposes a fast algorithm which can solve total variation and wavelet regularization based reconstruction model. By changing the iterative order of split Bregman algorithm and utilizing the connection between the projection operator and the shrinkage operator, the iteration form of the proposed algorithm is more compact than split Bregman algo-rithm. The proposed algorithm avoids to solve Laplace type partial differential equation, therefore, it has low computational complexity and can accelerate the reconstruction computation.It is known that total variation and wavelet regularization based reconstruction model has good effect for piecewise smooth images but don’t fit for non-piecewise s-mooth. This dissertation proposes a second-order total variation and wavelet regular-ization based reconstruction model which can solve that issue effectively. In addition, because the proposed model involves high-order Euler-Lagrange equation whose solu-tion includes complex numerical computation. By combining twice variable splitting scheme and alternating direction method of multipliers, this dissertation converts pri-mal high-order problem to several low-order problems and then solve them one by one. This reconstruction algorithm can effectively reduce the calculational complexity and improve the construction speed.By applying the forward-backward operator splitting technology, this dissertation proposes a fast reconstruction algorithm for solving the sparse parallel imaging problem with huge computation. This algorithm doesn’t involve complex computation of partial differential equation corresponding to primal problem, so its calculational effectiveness doesn’t depend on the special property of sparse operator and encoding operator (that is the system matrix can be diagonalized by fast Fourier transform). The effectiveness of the proposed algorithm is more obvious in the reconstruction experiments for big scale multi-channel signal data. Moreover, this dissertation analyzes the convergence of the proposed algorithm.