Compressed MRI Reconstruction Exploiting a Rotation-Invariant Total Variation Discretization
This work addresses image quality and computational efficiency in MRI reconstruction for medical imaging, representing an incremental advance by integrating existing techniques with tailored optimization.
The authors tackled compressed MRI reconstruction by proposing a variational framework that combines a rotation-invariant total variation discretization with BM3D sparsifying transforms, resulting in significant performance improvements over state-of-the-art methods and eliminating stagnation issues in previous BM3D-MRI approaches.
Inspired by the first-order method of Malitsky and Pock, we propose a new variational framework for compressed MR image reconstruction which introduces the application of a rotation-invariant discretization of total variation functional into MR imaging while exploiting BM3D frame as a sparsifying transform. In the first step, we provide theoretical and numerical analysis establishing the exceptional rotation-invariance property of this total variation functional and observe its superiority over other well-known variational regularization terms in both upright and rotated imaging setups. Thereupon, the proposed MRI reconstruction model is presented as a constrained optimization problem, however, we do not use conventional ADMM-type algorithms designed for constrained problems to obtain a solution, but rather we tailor the linesearch-equipped method of Malitsky and Pock to our model, which was originally proposed for unconstrained problems. As attested by numerical experiments, this framework significantly outperforms various state-of-the-art algorithms from variational methods to adaptive and learning approaches and in particular, it eliminates the stagnating behavior of a previous work on BM3D-MRI which compromised the solution beyond a certain iteration.