MRI Reconstruction Algorithms Based On Compressed Sensing

In clinical medical imaging, Magnetic Resonance Imaging (MRI) is one of the most important imaging modalities for its excellent depiction of soft tissues, absence of emitted ionizing radiation and the arbitrary imaging. Apart from its advantages, the relationship between the number of measured data samples and net scan time is hard to balance. In clinical imaging, increased scan duration means more data for reconstruction, but presents a number of problems including higher susceptibility to physiological motion artifacts, diminished clinical throughput, and added patient discomfort. In MRI the received data corresponds to the Fourier transform of the image, the conventional MRI scan provide the line by line sampling scheme, that result in the frequently cutover of the gradient of phase encoding. To overcome the limitation and reduce the measurement time, one should develop a novel reconstruction method that allows for reasonable reconstruction from clearly reduced measured data. As a fundamental problem in the MR imaging, reconstruction is one of the earliest and most classical linear inverse problems and has been extensively studied in the past two decades. The emerging novel theory in signal processing called Compressive Sensing which offered the opportunity for when and how a signal can be restored to reasonable resolution even when the sampling ratio is significantly lower than that suggested by the Nyquist Sampling theory.Compressive Sensing is mainly consisting of three parts:Sparse representation; Sampling matrix; Reconstruction Algorithm. In this work, a novel Compressive Sensing based method which allows for successful reconstruction from sparse sampling is proposed, and two aspects is included in this thesis.Firstly, we proposed a novel Split Augmented Lagrangian Shrinkage Algorithm under the framework of Alternation Directing Method. The split and penalty idea is widely used in a wide range of CS-based inverse problem, apart from the former ADM based methods which how to solve the involved sup-problem efficiently or replace the penalty parameter with self-adaptive one, this work propose a modified descent type alternating direction method (ADM) for MRI reconstruction in the following sense:a preliminary iteration result generated by the ADM is utilized to generate a descent direction; an appropriate step size along this descent direction is identified; and the penalty parameters are updated. The proposed method combined the advantages of both ADM and descent method, which has a faster convergence speed. At each iteration, the proposed method involves a thresholding/shrinking operator for one sub-problem and uses linearization and proximal point techniques to solve the other resulting sub-problem. Then, a descent direction, an appropriate step and the relaxation factor are derived. Finally, the penalty parameter is updated according to the convergence information. We demonstrate the effectiveness of the proposed algorithm by numerical examples and compare it with the state-o f-the-art algorithms.Secondly, we proposed a LO-norm based reconstruction method. In MR imaging filed L1-norm based optimal method is widely used as the reconstruction algorithm. Although the classical L1-norm based techniques achieve impressive results, they inherently require a degree of over-sampling to achieve exact reconstruction. When fewer measurements are given, the reconstruction generated by classic L1-normal based method becomes terrible. But, when the regularization is closed to LO-norm, the quality of reconstructed image can be obviously improved. The proposed method uses the Alternating Direction Method (ADM) to solve the unconstrained Augment Lagrange problem. The problem is first reformulated as the famous Augment Lagrange Function, and then alternatively minimized by ADM. Numerical comparison indicates that the proposed method can obviously improve the reconstruction quality, especially in highly under-sample condition.