Research On Compressed Sensing And Deep Learning Magnetic Resonance Image Reconstruction Based On The L_p-norm

Nowadays,Magnetic Resonance Imaging(MRI)is an indispensable clinical di-agnostic tool.It has no ionizing radiation,offers good soft-tissue contrast and multi-directional imaging.However,its development is limited by its slow imaging speed.To overcome the drawback,Compressed Sensing(CS)theory is developed to accelerate the speed of MRI.It can reconstruct images of high quality from under-sampled k-space data,thus shorten the imaging time.CS-MRI mainly includes three aspects,which are sparse representation,sampling method and image reconstruction algorithm.CS utilizes the sparsity of images in some transform domains and uses the sparse representation as prior information to reconstruct the image.In the traditional CS-MRI model,Total Variation(TV)was applied to en-hance sparsity.However,traditional TV based on the l1 norm is not the most direct way to induce sparsity and it cannot offer a sufficiently sparse representation.There-fore,this paper proposes two new regularizations for the deficiency of traditional TV and introduces them to the reconstruction model.Since the lp-norm(0<p<1)promotes the sparsity better than that of the l1-norm,we propose two extended TV algorithms based on the lp-norm:anisotropic and isotropic total p-variation(TpV).Then we introduce them to the MRI reconstruction model.We apply the Bregman iteration technique to handle the proposed optimization problem.During the iteration,the p-shrinkage operator is employed to resolve the nonconvex problem caused by the lp-norm.Experimental results illustrate that the proposed algo-rithms could offer the higher SNR and lower relative error compared with traditional TV algorithms and high-degree TV(HDTV)algorithm in MRI reconstruction problem.In addition,inspired by the application of the lp-norm in CS,we introduce this norm into Deep Learning(DL).We combine it with the common mean square error(MSE)loss function as a new loss function.It is introduced into U-net network to ac-celerate MRI reconstruction.Fast automatic reconstruction is completed by learning a large number of under-sampled MR images.Experimental results show that compared with the three common loss functions,the proposed network shows superior perfor-mance under different sampling templates and sampling rates.It improves the quality of reconstructed images,suppresses background noise,captures detail information and it can perform batch reconstruction of MR images.