Dynamic MRI reconstruction exploiting blind compressed sensing combined transform learning regularization

Abstract The goal of dynamic magnetic resonance imaging (dynamic MRI) is to visualize tissue properties and their local changes over time that are traceable in the MR signal. Compressed sensing enables the accurate recovery of images from highly under-sampled measurements by exploiting the sparsity of the images or image patches in a transform domain or dictionary. In this work, we focus on blind compressed sensing (BCS), where the underlying sparse signal model is a priori unknown, and propose a framework to simultaneously reconstruct the underlying image as well as the unknown model from highly under-sampled measurements. Specifically, in our model, the patches of the under-sampled images are approximately sparse in a transform domain. Transform learning that combines wavelet and gradient sparsity is considered as regularization in our model for dynamic MR images. The original complex problem is decomposed into several simpler subproblems, then each of the subproblems is efficiently solved with a variable splitting iterative scheme. The results of numerous experiments show that the proposed algorithm outperforms the state-of-the-art compressed sensing MRI algorithms and yields better reconstructions results.