Research On Application On Compressed Sensing In Reconstruction Of Complex Signals And MR Images

Magnetic resonance imaging(MRI)is a noninvasive imaging method,which is an important tool for medical research and diagnosis of orthopedic,neurological,cardio-vascular,and oncological.MRI offers high spatial resolution and excellent soft tissue contrast without employing ionizing radiation.However,since the acquisition mecha-nism of MRI is based on sequentially probing the interactions between nuclear atom spins and a changing magnetic field,so the acquisition speed is relatively slow.Low acquisition speed not only causes discomfort of patients but also seriously affects MRI quality and clinical throughput.Although modern MR scanners have been designed to improve the speed of data acquisition through hardware and pulse sequence,it is still constrained by physical and psychological aspects of patients.Recently,undersampled k-spatial data has commonly been used to reduce the data acquisition time,however,inadequately acquired k-space data will cause artifacts and affect diagnostic result.Therefore,it is of both theoretical and practical significance to develop reliable methods to reconstruct MR images accurately.The emerging com-pressed sensing(CS)theory,as a new type of sampling theory,predicts that sparse sig-nals and images can be reconstructed from highly undersampled measurements,which breaks through Nyquist/Shannon sampling limitation and provides a new way for fast MRI.In this thesis,based on the deeper research of the related theories of MRI and CS,we study the recover of-D sparse complex signals and the reconstruction technology of CS-MRI,the main work and innovations are summarized as follows:(1)Since l1Minimization methods needs a large number of samples to reconstruct sparse complex signals,we propose a strategy that separating complex numbers into real parts and imaginary parts and then use l1-Minimization with this strategy to reconstruct the sparse complex signals to reduce the number of samples.In addition,for solving the least square problem in OMP algorithm,a Landweber method with several different parameter selection schemes is applied into OMP.Numerical simulations show that l1-Mimization with the proposed strategy can accurately recover the complex signal with much fewer samples and the proposed Landweber method is efficient.(2)In order to overcome the deficiencies that the traditional two-dimensional wavelet transform can not provide the optimal representation for MR images,two new joint sparse representation methods(combined wavelet and Contourlet,combined wavelet and Shearlet)are proposed respectively.Besides,to overcome the artifacts due to insufficient sampling,similarity prior of MR images is exploited to achieve fast re-construction.For two joint sparse transforms using similarity prior,two new models and their corresponding algorithms are proposed.Numerical results indicate that the proposed methods have high accuracy and high signal to noise ratio.Compared with the methods using only wavelet,Contourlet,or Shearlet,more detail information such as boundaries,corners,and contours can be reconstructed by using our joint sparse transformation.Moreover,exploiting similarity within a series of MR images saves acquisition time.Furthermore,the proposed algorithms outperform the state-of-the-art algorithms(CG,RecPF,TVCMRI,FCSA,WaTMRI)based on standard sparsity and patch-based algorithm(PANO for CS-MRI in terms of both the number of measure-ments and reconstruction speed.(3)Considering the slow speed of acquisition,the unsatisfactory reconstruction quality of MR image,and the high computational complexity of existing reconstruction algorithms,two efficient algorithms using similarity prior based on NESTA and AD-MM frameworks are proposed.In order to validate the benefit of the similarity prior based on reference for longitudinal CS-MR image reconstruction,we compare them with the state-of-the-art algorithms(CG,RecPF,TVCMRI,FCSA,WaTMRI)based on standard sparsity.In order to investigate the effectiveness of the proposed algorithms,we compare them with frbCSLMRI based on similarity prior.Numerous experiments demonstrate the superious performance of the proposed algorithms for compressed MR image reconstruction in terms of both accuracy and visual quality.The complexities of our methods are much lower than that of the frbCSLMRI method.