Research On Magnetic Resonance Reconstruction Algorithm Based On Compressed Sensing

Magnetic resonance imaging equipment（Magnetic Resonance Imaging,MRI）is an important modern medical diagnosis system,which has been widely used in clinical disease diagnosis.However,due to its relatively long scanning time,the patient is more prone to movement during scanning,which affects the image quality.At the same time,the scanning speed also limits its application in some special clinical scenarios,such as cardiac scanning and multi-dynamic enhanced scanning.Parallel imaging and compressed sensing are two representative technologies to increase the scanning speed.Parallel imaging technology uses multi-channel coils to speed scanning.Compressed sensing takes advantage of the sparse nature of the signal in certain transform domains to collect fewer K-space points than traditional methods.And so the scanning speed is increased greatly.Therefore,how to combine parallel imaging and compressed sensing to provide an effective reconstruction algorithm,and on the premise of ensuring image quality and resolution,further increase the scanning speed has become a research difficulty in the field of magnetic resonance.This thesis mainly studies how to combine the compressed sensing algorithm with the parallel imaging algorithm to improve the speed of magnetic resonance scanning.The self-calibration parallel imaging method SPIRi T is a novel parallel acquisition algorithm based on the general automatic calibration part parallel acquisition algorithm GRAPPA,which explicitly uses the multi-channel coil sensitivity to convert the parallel imaging reconstruction method into a nonlinear optimization problem.This thesis has conducted a series of studies based on the SPIRi T reconstruction framework.First,under the constraints of data fidelity,the image is transformed into a sparse domain,the minimum value of the l₁-norm is obtained for the sparsely transformed image,and a reconstructed image of undersampling magnetic resonance data is reconstructed.Secondly,in order to improve the reconstruction quality of the SPIRi T framework,the traditional Tikhonov regularized SPIRi T is improved.The traditional Tikhonov regularization term in SPIRi T is changed to the l₁-norm regularization.The results show that the improved SPIRi T algorithm has better reconstructed image quality than the traditional SPIRi T.It can significantly reduce artifacts,and is more robust.Finally,combining compressed sensing and parallel imaging,a total variation（TV）regularization is added to the improved SPIRi T framework.In order to solve the problem with two non-smooth terms,the thesis proposes a convex optimization iterative algorithm based on primal-dual frame.The algorithm solves the problem with multiple non-smooth terms by simultaneously solving the original optimization problem and its dual problem.So the image reconstruction can be realized by iteration.The results prove that images with higher signal-to-noise ratio and lower reconstruction artifacts can be obtained by using the compressed sensing combined with parallel imaging algorithm proposed in this thesis.So the reconstruction image quality can be greatly improved.