Fast Alternating Minimization Method for Compressive Sensing MRI under Wavelet Sparsity and TV Sparsity

In this paper, we extend the alternating minimization algorithm proposed in [ Y. G. Zhu and X. L. Yang, Journal of Signal and Information Processing, 2 (2011), pp. 44-51] to compressive sensing MRI model with wavelet sparsity and total variation(TV) sparsity simultaneously. This extended approach can reconstruct the MR image from under-sampled k-space data, i.e., the partial Fourier data. We also give the convergence analysis of extended alternating minimization method. Some MR images are employed to test in the numerical experiments, and the results demonstrate that the alternating minimization method is very efficient in MRI reconstruction.