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Abstract #3411

A fast algorithm for tight frame-based nonlocal transform in compressed sensing MRI

Xiaobo Qu 1 , Yunsong Liu 1 , Jing Ye 1 , Di Guo 2 , Zhifang Zhan 1 , and Zhong Chen 1

1 Department of Electronic Science, Xiamen University, Xiamen, Fujian, China, 2 School of Computer and Information Engineering, Xiamen University of Technology, Xiamen, Fujian, China

Compressed sensing magnetic resonance imaging (CS-MRI) is to reconstruct MR images from undersampled k-space data by enforcing the sparsity of MR images. Patch-based nonlocal operator (PANO) is proposed as a linear operator to exploit the nonlocal self-similarity of MR images to further sparsify them. However, the original PANO is a frame and its numerical algorithm for CS-MRI problem is solved by the alternating direction minimization with continuation (ADMC). These two aspects lead the reconstruction to be time consuming. In this work, we first convert the PANO into a tight frame, and then applied the alternating direction method of multipliers (ADMM) algorithm to accelerate the image reconstruction. The empirical convergence demostrates that the new approach significantly accelerate the image reconstruction in compressed sensing MRI and can accomplish the reconstruction of one 256256 within several seconds.

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