Fast MRI Image Reconstruction Based On Compressed Sensing

Magnetic Resonance Imaging(MRI) is one of the important means of medical imaging, compare with Computer Tomography(CT), MRI has the advantage of nonionizing radiation, and can image all kinds of soft tissue, such as the heart and blood vessels. MRI also has its limits: the slower data scanning speed has been restricting further development of MRI and the other problems arising from this also has a lot. First, the slower imaging speed will reduce the utilization rate of MRI scanner and increase the cost of inspection; it is not making for the generalization of MRI. Second, MRI was conducted in a relatively closed space, and then the long imaging time may make patients grow a feeling of claustrophobic fear, thus produce involuntary movement, eventually the quality of image is affected. Therefore, in the case of taking into account of image quality, looking for a fast imaging method is the problem to be solved. As a new theory of signal acquisition and processing, compressed sensing(CS) is able to recover the sparse signal accurate approximately from a few measurements. In order to solve the problem of the slower imaging speed,compressed sensing theory is applied to MRI, and then the existing nonlinear reconstruction algorithm is improved and an efficient noncoherent measurement matrix is designed.Based on Bregman iterative algorithm, Split Bregman iterative algorithm separates the1 l and2l portions of the objective function that greatly reduce the computational complexity and speed up the convergence time of the algorithm. But the reconstruction quality needs further improvement. Based on Split Bregman iterative algorithm, we use the total variation, short support wavelet and high vanishing moment wavelet as the regularizations to reconstruct the CS_MRI images. So it can fully exert the sparsity of different characteristicsof MR images in different transform domain. Thus, the reconstruction quality can be improved in the situation of the same measurement data.The measurement matrix is required to meet the incoherence with sparse transform matrix, satisfy the distribution of MRI data of large amplitude in k space center and small amplitude in k space periphery, and easy to hardware implementation. Due to the purely random under-sampling scheme is impractical in hardware design, so the random measurement matrix commonly used in compressed sensing theory is no longer applicable. In this thesis, the inherent pseudo randomness and the external deterministic characteristics of chaotic systems are used for designing a chaotic measurement matrix. The pseudo randomness satisfies the requirement of incoherence, and the deterministic satisfy the requirement of easy to hardware implementation.Compared with spiral, chaotic measurement matrix has better incoherence. The reconstruction quality can be better with the same measurement data.