The Magnetic Resonance Image Reconstruction Methods Based On Compressed Sensing

Compressed sensing is a new signal processing theory which is put forward recent years.It is characterized by accurately reconstructing signal under the condition of low sampling rate.Since proposed it has been received widespread attention and become hotspots.Recently,compressed sensing has applied to many fields;one of the most classic applications is that it was applied to magnetic resonance imaging,especially in the dynamic magnetic resonance imaging.Magnetic resonance imaging was conducted by K space data sampling and through a series of data processing finally presenting the weighted images.In medical practice,in order to get accurate image,patients often need to keep body static while scanning.But maintain a state for a long time will produce fatigue or even shaking.This involuntary jitter will leads to artifacts.So how to shorten the scan time and accelerate the data acquisition is most important.The combination of compressed sensing and magnetic resonance imaging which using only a tiny amount of K space data to reconstructed can greatly reduce the scanning time.For dynamic magnetic resonance imaging,there are highly correlated among frames.The background component has little change,while the dynamic component is rapidly changing over time.This is similar to the video sequence,so the low rank matrix theory which is used for video modeling is suitable for dynamic magnetic resonance imaging reconstruction.Considering each temporal frame as a column of a space time matrix,through which we produce a low-rank matrix.By taking low-rank and Sparse matrix decomposition we can reconstruct the original image as well as the low-rank and sparse components.Using low-rank and Sparse matrix decomposition model for dynamic magnetic resonance image reconstruction,this paper first introduce the application of Iterative Soft Threshold(IST)algorithm for dynamic Magnetic Resonance Imaging reconstruction.Considering this method exists two problems: the poor reconstruction accuracy and converge speed,two measures have been taken.On the one hand,Accelerate the proximal gradient method(APG)and Inexact Augmented Lagrangian Method(IALM)have been introduced for fast reconstruction.On the other hand,in order to achieve high precision,Total Variation(TV)regularization based on low-rank and sparse decomposition model has been introduced to further remove noise and artifacts.In order to verify the effectiveness of the proposed methods,the simulation about reconstruction of cardiac perfusion MRI and cardiac cine MRI has been done.The result of the simulation demonstrates that: using APG and IALM for Low-rank and Sparse matrix decomposition reconstruction result in higher reconstruction performance than IST method,besides,IALM is more superior to the APG algorithm.Although introducing TV regularization reduces the reconstruction speed than IALM,it still fast than IST and the reconstruction accuracy is higher than IALM.