Image reconstruction of compressed sensing MRI using graph-based redundant wavelet transform

• Image patches is viewed as vertices and their differences as edges, and the shortest path on the graph minimizes the total difference of all image patches.
• A graph-based redundant wavelet transform (GBRWT) to sparsely represent MR images is proposed.
• A GBRWT-based undersampled MR image reconstruction method is proposed. Simulation results with added noise demonstrate the superior de-noising capacity of the proposed method.
• Simulation results on in vivo data demonstrate that the proposed method achieves lower reconstruction error and higher visual quality than several state-of-the-art CS-MRI methods.

Compressed sensing magnetic resonance imaging has shown great capacity for accelerating magnetic resonance imaging if an image can be sparsely represented. How the image is sparsified seriously affects its reconstruction quality. In the present study, a graph-based redundant wavelet transform is introduced to sparsely represent magnetic resonance images in iterative image reconstructions. With this transform, image patches is viewed as vertices and their differences as edges, and the shortest path on the graph minimizes the total difference of all image patches. Using the l1 norm regularized formulation of the problem solved by an alternating-direction minimization with continuation algorithm, the experimental results demonstrate that the proposed method outperforms several state-of-the-art reconstruction methods in removing artifacts and achieves fewer reconstruction errors on the tested datasets.

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