MRI Reconstruction Algorithms Based On Compressed Sensing

Magnetic resonance imaging (MRI) plays an important role in medical diagnosis and scientific research, which is a noninvasive, nonionizing and high contrast imaging technique. However, the main limitation of MRI is that it is a relatively slow imaging modality especially the data sampling time during imaging process. A variety of MR techniques aim to reduce the number of data required for accurate reconstruction in order to reduce the sampling time cost.The development of the theory of compressed sensing allows greatly reduce the amount of data needed to sampling. Compressed sensing theory provides effective way for reconstruction magnetic resonance images using the incomplete K space sampling data. Using essentially the characteristics of the image can be represented by the sparse and a variety of prior knowledge of the image itself to constraint solving model for reconstruction. This dissertation is focused on exploring the image sparse representation and a variety of priori regularization terms used in image reconstruction models so that the amount of data sampled and the time required for sampling the magnetic resonance imaging can be reduced.The main contents of this dissertation are listed as follows:1. The algorithms based on sparsity prior and total variation regularization can reconstruct various images, but these algorithms cannot reconstruct textures, edges and other structures in image effectively due to the fact that the total variation regulation is based on the assumption that local image patches are smooth. To improve these problems, this dissertation makes use of the similarities between the reconstructed sparse coefficients and the sparse coefficients of original image as the prior. Then the non-local sparse representation regularization model is formed based on non-local similarity between patches and sparsity representation. Experiments show that the proposed algorithm can achieve a better reconstruction performance than the conventional ones.2. Sparse representation in traditional image reconstruction does not take into account the structure in the data space. Especially when the sparse representation dictionary is formed merely using the subsampling data, image cannot be sparse represented effectively. To solve this problem, this dissertation makes fully use of the local geometry in the data space and emphasize the correction among image patches by adding the graph regularization to the sparse representation model. So the image can be better sparse represented by the dictionary. Experiments show that the proposed algorithm can achieve a better reconstruction performance than the traditional methods. The relationship between the quality of the reconstructed MR images and different type of sampling matrix, and different subsampling rate is discussed.