Tight Frame Based Weighted Sparse Reconstruction For Magnetic Resonance Image

Magnetic Resonance Imaging(MRI)is a non-invasive and non-radioactive imaging method,which is widely used in clinical diagnosis.However,long scanning time is difficult to capture the rapid signal changes,and will lead to artifacts in the imaging of moving parts.Therefore,reducing scanning time while obtaining highquality magnetic resonance(MR)images is the goal of academia and industry.Compressed Sensing MRI(CS-MRI)is an important way to accelerate MRl.One of the key points of developing CS-MRI reconstruction methods is the sparse representation.Sparse representation can be divided into two main categories:orthogonal sparse representation system and redundant sparse representation system.The latter is mainly represented by tight frame which can capture more image features to better suppress noise and artifacts.Under tight frame sparse representation,there are two different models called synthetic model and analysis model.The latter can achieve lower reconstruction error.To solve the analysis model,Qu et al proposed a simple and efficient algorithm named projected fast iterative soft-thresholding algorithm(pFISTA).However,current research on pFISTA mainly concentrated on the reconstruction under Cartesian under-sampling.The reconstruction problem and application under the nonCartesian under-sampling have not been involved.Dynamic contrast-enhanced MRI(DCE-MRI)can evaluate the morphological characteristics and microvascular hemodynamic characteristics.It has been widely used to detect tumor severity and evaluate treatment response of targeted drugs.Traditional Cartesian sampling for DCE leads to low time resolution and cannot capture complete dynamic changes.In recent years,non-Cartesian golden-angle radial sampling has been used to achieve DCE-MRI with high temporal resolution.However,existing methods remains long reconstruction time.Besides,under high acceleration factor(AF),these methods suffer from high reconstruction error,much noise and artifacts,and low fidelity of dynamic quantitative parameters Ktrans and Vp.For DCE-MRI,this thesis proposed a spatiotemporal separation weighted sparse reconstruction model.Weights were introduced to distinguish the importance of spatial and temporal sparsity.We derived pFISTA to be suitable for solving the proposed nonCartesian reconstruction model and theoretically proved the convergence condition of pFISTA under non-Cartesian reconstruction.Results on both the brain tumor DCE and liver DCE show that,at relatively high AF,the lowest reconstruction error and highest image structural similarity are obtained by the proposed method.Besides,the proposed method achieves faster reconstruction for liver datasets and better physiological measures on brain tumor images.For static MRI,the existing tight frame-based reconstruction models do not distinguish different sparse coefficients,which leads to the loss of image details.Therefore,this thesis proposed a weighted sparse reconstruction model.Weights were introduced to distinguish the importance of the sparse coeffcients in sparse transform domain.We derived pFISTA to be suitable for solving the proposed model and proved the convergence condition of pFISTA under weighted l1 norm reconstruction.Experimental results on brain data show that the proposed method achieves the lowest reconstruction errors under different under-sampling patterns and sampling rates.