Research On Compressed Sensing Oriented To MR Image Reconstruction

In the magnetic resonance imaging system, in order to collect enough K space signals, the gradient for phase encoding must continually change, consequently the scanning time is prolonged. As an emerging signal sampling and reconstruction theory, compressed sensing breaks through the sampling limitation set by Shannon’s theory. By exploiting the internal structure characteristics and regulating the transform sparsity of the target signal, much fewer samples are required to accurately recover a signal compared to the conventional methods. Therefore, compressed sensing provides a new way to settle the time-consuming sampling problem in MR imaging. With a small quantity of randomly collected samples in K space, by adding transform sparsity regulation in the reconstruction algorithm, the clear medical imaging can be achieved.There are three kept points in compressed sensing:the sampling matrix, the sparsifying transform and the reconstruction algorithm. In this work, to accurately recover the MR images, by using the support-based compressed sensing, distributed compressed sensing and three-dimensional compressed sensing methods, various sparsifying transforms and reconstruction algorithms are proposed.Firstly, by analyzing an existing singular value decomposition-based sparsifying transform, the distribution patterns of the large coefficients in the sparse representation are observed. Using the support-based compressed sensing method, a special support detection method is proposed for the singular value decomposition-based sparse representation. In addition, a reconstruction algorithm Support-FCSA is proposed with the combination of the support-based compressed sensing method.Secondly, by treating multiple coil system as a special distributed sensor system, with the distributed compressed sensing method, a shared singular value decomposition-based sparsifying transform is proposed to fully explore the structure similarities between different coil images, then a reconstruction method for multiple coil images is presented and named as DCS-SENSE.Thirdly, by organizing the multiple coil images as a three-dimensional tensor, inspired by the three-dimensional compressed sensing method, the Walsh sparsifying transform is suggested to synchronously reduce the inter-coil and intra-coil redundancies and consequently to enforce transform sparsity in three dimensions. In the meantime, the multiple coil image reconstruction method11-SPIRiT is improved as the11-SPIRiT-FCSA method. To summarize, this dissertation reports the author’s work on the compressed sensing theory to pursue MR image reconstruction from highly under-sampled K space. The combination of support-based method and SVD-based sparsifying transform is capable of finding the more accurate sparse representations of the target images. The shared SVD-based sparsifying transform and the3D Walsh sparsifying transform are developed to fully exploit the inter-coil information relativity. The reconstruction methods based on these three sparsifying transform, i.e. Support-FCSA, DCS-SENSE and11-SPIRiT-FCSA, were tested on various datasets, sampling patterns and reduction factors, reliable images were reconstructed with the proposed methods.