RESUMEN
Purpose: To develop a synergistic image reconstruction framework that exploits multicontrast (MC), multicoil, and compressed sensing (CS) redundancies in magnetic resonance imaging (MRI). Approach: CS, MC acquisition, and parallel imaging (PI) have been individually well developed, but the combination of the three has not been equally well studied, much less the potential benefits of isotropy within such a setting. Inspired by total variation theory, we introduce an isotropic MC image regularizer and attain its full potential by integrating it into compressed MC multicoil MRI. A convex optimization problem is posed to model the new variational framework and a first-order algorithm is developed to solve the problem. Results: It turns out that the proposed isotropic regularizer outperforms many of the state-of-the-art reconstruction methods not only in terms of rotation-invariance preservation of symmetrical features, but also in suppressing noise or streaking artifacts, which are normally encountered in PI methods at aggressive undersampling rates. Moreover, the new framework significantly prevents intercontrast leakage of contrast-specific details, which seems to be a difficult situation to handle for some variational and low-rank MC reconstruction approaches. Conclusions: The new framework is a viable option for image reconstruction in fast protocols of MC parallel MRI, potentially reducing patient discomfort in otherwise long and time-consuming scans.
RESUMEN
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.
