Undersampled Dynamic MRI Reconstruction Based On Sparsity And Low-rank Regularization

Dynamic magnetic resonance imaging(MRI)can be used to diagnose organs'motion,so it is useful and has been used widely in clinical diagnosis.However,the MRI process usually takes a long time to scan,this drawback restricts the achievable spatiotemporal resolution in dynamic MRI.Therefore,a popular theory called compressed sensing(CS)has been introduced to reduce the scan time,it exploits the fact that a signal can be reconstructed perfectly from incomplete measurements when it is sparse or transform sparse.So reconstructing dynamic MRI from undersampled measurements can accelerate the imaging speed.In recent years,low-rank matrix completion extends the idea of CS from vectors to matrices,enabling recovery of missing or corrupted entries of a matrix under low-rank condition.Due to the correlation between the frames of the dynamic MRI sequence,the idea of the low-rank matrix completion can be applied to the reconstruction of the dynamic MRI.The main focus of this paper is how to reconstruct the undersampled dynamic MRI using CS and low-rank matrix completion theory.The main work is as follows:Firstly,we propose a dynamic MRI reconstruction method which utilizes the redundancy in local and global domains jointly.For dynamic MRI,there is much correlation in spatial and temporal dimensions,and if the spatial and temporal redundancy can be utilized efficiently in the reconstruction process,higher spatial and temporal resolutions can be achieved.In this paper,a 2-D matrix is obtained by vectorizing the images in every frame of a 3-D dynamic MRI sequence,and we extract overlapping 2-D patches from this matrix.For each patch,its similar patches will be searched within a local window with fixed size from these 2-D patches,and a non-convex function is used to approximate the low-rank matrix formed by these similar patches.At the present stage,the local correlation in the temporal dimension is employed sufficiently.To obtain better image quality,the global correlation in the temporal dimension is utilized by a low-rank penalty which is relaxed by the nuclear nOorm.At last,we validate the superior reconstruction performance of the proposed algorithm by comparing to existing state-of-the-art methods.Secondly,we propose a dynamic MRI reconstruction method which bases on low-rank regularization and 3D sparsifying transform with separation of background and dynamic components.Due to the dynamic MRI is similar to the video sequences.it can be inherently represented as a superposition of background components and dynamic components,so we decompose it into two parts of background and dynamic components based on robust principal component analysis(RPCA)algorithm.For background components,a patch-based non-convex low-rank function is used to penalize it,and for dynamic components,we penalize it by using a 3D sparsifying transform.The proposed optimization problem is solved by variable splitting and alternative optimization,then the background and dynamic components can be obtained,we just need to add these two parts.Numerical experiments indicate that the proposed method can recover clearer images and preserve details better.