Algorithm Research On Reconstruction For Dynamic Magnetic Resonance Imaging From Undersampled K-Space Data

As a non-damage detection technology,Magnetic Resonance Imaging(MRI)is becoming one of the most important detection methods for clinical disease diagnosis by non-ionizing and non-radiation injury to the human body.Howerver,limited by various imaging conditions,the drawback of MRI is that the scanning time is prolonged consequently.In the scanning process,since the patient needs to maintain a certain posture for a long time,which will cause the discomfort for the patient,and is easy to cause the motion artifacts during the imaging.Dynamic MRI(dMRI)is a kind of motion imaging technology that can acquire movies of human tissues and organs through scanning continuously and rapidly.The charaters of dMRI are high spatial resolution and temporal resolution.Compared with the static MRI,dMRI need higher requirements.For a long time,how to shorten the time of MRI scanning and improving the speed of MRI has been a problem for the MRI researchers,because they cannot overcome the limitations of Nyquist sampling law.The theory of Compressive Sensing(CS),has been proposed in 2008,which makes it possible to recover and reconstruct MRI images from highly undersampled k-space data by utilizing the inherent sparsity of MRI image data.Howerver,the straight-forward extension of CS-MRI technology to applications such as free breathing cine and free breathing myocardial perfusion MRI often results in poor performance since the method of sparse representation in traditional CS algorithms can not sparsify data enough in spatio-temporal.To overcome this problem,a method named blind dictionary learning for the accelerating dMRI image reconstruction has been proposed to estimate simultaneously a dictionary of spatio-temporal basis functions and coefficients directly from the undersampled k-t space data.In addition,to reduce the computational complexity and the over-training for atoms in dictionary learning under the framework of CS theory.Two methods of reconstruction for dynamic MRI based on low-rank and sparse matrix decomposition model relying on the low-rank structure of the spatio-temporal data are respectively proposed in this paper.One of the two methods is convex optimization and the other is non-convex optimization.Those methods are used to accelerate image reconstruction and improve the quality of dynamic MRI image reconstruction from undersampled k-t space data.The main contribution of this paper can be summarized as follows:1)We present an image reconstruction method for dynamic MRI based on blind dictionary learning.The blind dictionary is established by learning from the highly undersampled k-t space of the dMRI,which can be used to tansform the images and abtain the sparse representation of dynamic MRI.We also proposed a solution to the optimization problem that joints the dictionary learning and the sparse representation of dynamic MRI by using the minimum optimization algorithm.This mothod is mainly to get rid of the limitation of measurement matrix that used in the classical CS and blind compressed sensing based on K-SVD dictionary learning,which decreases the computing complexity when the traditional convex optimization methods directly solve the sparse coefficients from high dimensional matrix.Tested on two dMRI datasets of reconstruction,the proposed method performs better than the compared method in the image reconstruction performance under the same sampling acceleration factor.2)We propose an image reconstruction method for dynamic MRI by using a kind of truncated nuclear norm to solve the robust principal component analysis.The method can decrease the image reconstruction error that caused by directly using the nuclear norm to optimize the non-convex rank function in the model of low-rank and sparse matrix decomposition.The proposed method,TNN-RPCA,uses the truncated nuclear norm instead of traditional nuclear norm to optimize the rank function,and depends on the Inexact Augmented Lagrange Multiplier(IALM)to solve the RPCA problem fastly and accurately.Compared with two other methods for solving RPCA problem to reconstruct dynamic MRI images,the TNN-RPCA method has obvious advantages in terms of both the speed and the quality of image reconstruction.3)We also put forward a method named OptShrink-RPCA,by using optimal singular value shrinkage to resolve RPCA problem,for dynamic MRI images reconstruction.The OptShrink-RPCA is a kind of non-convex optimization method,which can solve the application defect for directly applying the nuclear norm to optimize the non-convex rank fuction.Firstly,the OptShrink-RPCA truncates the singular values of the measurement matrix.Secondly,the rest of the singular values after truncated are shrinked by threshold processing.Finaly,the IALM algorithm is been introduced to solve the RPCA problem acceleratedly.Compared with several convex optimization methods for dynamic MRI reconstruction,the OptShrink-RPCA method provides better performance of reconstruction images.