A Phase-Constrained Parallel Magnetic Resonance Imaging Reconstruction Algorithm Based On Low-Rank Matrix Completion

Magnetic Resonance Imaging (MRI) is an important modality among various medical imaging technologies. The problem on how to reduce the scanning time has received much attention during the past decades. Firstly, we introduce two traditional MRI reconstruction categories with short scanning time, constrained reconstruction and parallel imaging, whose several models in common use and their basic principles are analyzed. Then some methods are introduced in which the constrained reconstruction is combined with parallel imaging.The appearance and development of Compressive Sensing (CS) made it possible to fulfill MRI reconstruction under the traditional Nyquist sampling rate. MRI reconstruction models based on the completion of a low-rank data matrix are proposed in the fields of constrained reconstruction and parallel imaging. On the basis, we proposed a novel phase-constrained parallel MRI reconstruction model based on low-rank matrix completion. In this thesis, phase constraint for the single-coil MRI system was expanded to the parallel MRI system. Moreover, the linear dependent relationship was derived among three dimensional k-space signals. According to the aforementioned relationship, the reconstruction of sparse parallel imaging with smooth phase in the underlying magnetization image of each coil was formulated as the completion of a low-rank data matrix which is constructed by the k-space neighborhood and symmetric sample of the neighborhood center.The proposed model is compared with the state-of-the-art calibrationless parallel MRI reconstruction model. Experimental results for both simulated dataset and real dataset show the proposed model has better performance in terms of resolution enhancement, k-space sampling reduction and denoising capability and reconstruction time shortening.