Transform learning MRI with global wavelet regularization

Sparse regularization of the reconstructed image in a transform domain has led to state of the art algorithms for magnetic resonance imaging (MRI) reconstruction. Recently, new methods have been proposed which perform sparse regularization on patches extracted from the image. These patch level regularization methods utilize synthesis dictionaries or analysis transforms learned from the patch sets. In this work we jointly enforce a global wavelet domain sparsity constraint together with a patch level, learned analysis sparsity prior. Simulations indicate that this joint regularization culminates in MRI reconstruction performance exceeding the performance of methods which apply either of these terms alone.