Sparse MRI Image Reconstruction With Graph Wavelet Transform

Magnetic resonance imaging(MRI)is an essential medical imaging tool and has been widely applied in the clinic diagnosis.One of the major limitations of MRI lies in the inherently slow data acquisition process,which limits its application in fast imaging.Therefore,accelerating MRI is significantly important,especially for those imaging applications on restless patients.Compressed sensing breaks through the sampling limitations and needs fewer samples to reconstruct the target image compared with the number required by the Nyquist sampling rule.Thus,accelerating MRI by under-sampling k-space samples is possible with compressed sensing.In compressed sensing MRI,images are reconstructed by enforcing their sparsity in some transform domains using some nonlinear algorithms.One of the key points for applying compressed sensing to successfully reconstruct MRI image is:Images can be sparsely represented in a certain transform domain.In the present study,a graph-based redundant wavelet transform(GBRWT)is introduced to sparsely represent MRI images in iterative image reconstructions.With this transform,image patches are viewed as vertices and their differences as edges,and the shortest path on the graph minimizes the total difference of all image patches.Then,wavelet transform apply on this shortest-path-visit patches make coefficients sparser than on their original order.Images are reconstructed by the l1 norm regularized formulation with an alternating-direction minimization with continuation algorithm.Experiment result demonstrate that GBRWT achieves sparser representation than wavelet transform,and GBRWT-based MRI reconstruction achieves better reconstruction at the tested sampling rates.Achieving high acceleration factor is still challenging for compressed sensingMRI since image structures may be lost or blurred when the acquired information is not sufficient.Therefore,it is possible to incorporate extra knowledge to improve image reconstruction for highly accelerated MRI.Fortunately,multi-contrast images in the same region of interest are usually acquired in MRI protocols.We propose a new approach to reconstruct magnetic resonance images by learning the prior knowledge from these multi-contrast images with graph-based representations.We further formulate the reconstruction as a bi-level optimization problem to allow misalignment between these images.In summary,we propose a sparse transform training,as well as a bi-level optimization scheme to extract prior information from multi-contrast images for compressed sensing MRI.Experimental results demonstrate that the proposed approach improves the image reconstruction significantly and is practical for real world application since patients are unnecessarily to stay still during successive reference image scans.Besides,it is also valuable to further speed up multi-contrast MRI imaging system by simultaneously undersampling these images.We propose to train a Graph-based sparse representation from the undersampled data and then use this sparse representation to jointly reconstruct all multi-contrast images simultaneously.The Graph-based sparse training and joint reconstruction optimizes the reconstruction by using the optimal sparse representation for the target images as well as using the joint sparse property.The proposed Graph-based jointly reconstruction method can further improve the image quality than a sparse reconstruction for each single image,thus allowing higher accelerating factor for all images.