Research On Sparse Reconstruction Algorithm For MR Images Based On Compressed Sensing

Magnetic resonance imaging(MRI)is one of the most important medical tomographic imaging methods and plays an increasingly important role in modern clinical applications and scientific research.However,the slower data acquisition process in the magnetic resonance(MR)imaging process results in a longer imaging time,which limits the further application and development of MRI.Therefore,increasing the imaging speed becomes the biggest challenge in MR imaging technology.In MRI,rapid imaging can be performed by quickly acquiring k-space data.One method is to design a sampling trajectory that is more complex than Cartesian sampling,so that the sampling trajectories generated by each sampling sequence cover more k-space data.However,this imaging method is constrained by the hardware condition of the MR imager and the design of the sampling sequence,and the ideal sampling effect cannot be achieved in actual applications.Another fast MRI method is parallel magnetic resonance imaging(pMRI).It uses multiple coils to receive MR signals simultaneously and utilizes the spatial sensitivity difference of the coils instead of partial gradient encoding to reduce gradient encoding steps and save scan time.However,due to the aliasing artifacts caused by the pre-sampling and the difficulty of solving the inverse problems caused by the increase of the number of coils,pMRI can only get a small acceleration number in actual clinical applications to ensure the ideal MR image reconstruction quality.The compressed sensing(CS)theory developed in recent years provides another rapid MRI possibility:by exploiting the sparseness or compressibility of the MR image itself,the original MR image can be perfectly reconstructed by solving a non-linear convex optimization problem on the premise that only part of the k-space data is downsampled.In MRI,the transform domain of the MR image,ie,k-space,is a Fourier space.From the image compressibility,it can be seen that the MR image is compressible in the Fourier space.On the other hand,since a random distribution matrix is irrelevant to any other matrix,that is,when the MR downsampling matrix is a random matrix,MRI meets the two assumptions of the CS theory,so a rapid MRI method can be developed based on CS theory.In the past decade,the rapid MRI technology based on the CS theory has become a hot spot for MRI research.Such MRI technology is referred to as CS-MRI.Its mathematical core is to solve a non-linear convex optimization mathematical model for downsampled k-space data and use appropriate optimization iterative algorithm to solve it.Therefore,its research direction can be roughly divided into the construction of optimization model and the design of optimization algorithm.In view of the above two points,this paper mainly did the following work:First,in order to cope with the robustness of the algorithm caused by the fixed subproblem weight in the iterative algorithms of proximal operators,this paper proposes an approximate smooth iterative algorithm based on the original-dual framework.By solving the primal optimization problem and its dual problem at the same time,this algorithm avoids the robustness problem of the algorithm due to the decomposition of the primal problem into two subproblems in the proximaty operator class iterative algorithm.Second,in order to solve the problem of error accumulation in real-time dynamic MR image reconstruction,this paper proposes an idea that all MR images are reconstructed after using only the first frame of the dynamic MR sequence as a priori image,thus avoiding the accumulation of errors due to the lack of dynamic MR sequence overall information.At the same time,in order to solve the problem that the difference between the first frame MR image and the subsequent image frame is getting bigger and bigger,this paper proposes to use the dynamic TV and the wavelet Li norm of the currently reconstructed MR image as the sparse regularization terms in the reconstruction model.And using the previous iterative algorithm based on the primal-dual framework to solve the optimization model constructed.Third,this article adopts a brand-new definition of the image TV norm,called twice finer TV,this TV is defined on the twice finer grid of the image gradient domain,which can better represents the isotropy of the image than the traditional image TV.This paper proposes a new CS-mMRI optimization model based on twice finer TV,this model regards the joint twice finer TV of multi-contrast MR images and the joint wavelet L1 norm as sparse regularization terms,and using the previous proposed iterative algorithm based on the primal-dual framework to solve the optimization model.