Fast MR image reconstruction with orthogonal wavelet regularization via shift-variant shrinkage

Algorithms with Lipschitz bounds such as ISTA and FISTA are useful for solving optimization problems with sparsity-promoting regularizers. However, they can be slow in applications that involve shift-variant system matrices. One example of such an application is MRI with multiple sensitivity coils. We propose a reconstruction algorithm for wavelet regularized SENSE MR image reconstruction that exploits the spatial localization of the wavelet basis and the shift-variant behavior of the MR system matrix to accelerate algorithm convergence. Our results indicate that the proposed method is faster than state-of-the-art variable splitting algorithms in terms of convergence speed for a SENSE-type reconstruction problem even when the variable splitting methods are tuned carefully. Unlike variable splitting methods, the proposed method requires no convergence parameter tuning.