Fast Reconstruction for Sparse MR Images in Compressed Sensing

In this paper, we apply TV sparsifying MR image reconstruction method proposed in [ Y. G. Zhu and X. L. Yang, Journal of Signal and Information Processing, 2 (2011), pp. 44-51] to compressed sensing MRI model with wavelet sparsity. The fast method to reconstruct MR images with wavelet sparsity in compressed sensing is presented. This approach can exactly reconstruct the MR image from the partial Fourier data. The convergence of the fast method is analyzed. Some MR images are employed to test in the numerical experiments, and the results demonstrate that this method is very efficient in the reconstruction of MR images.