Title :
Augmented Lagrangian with Variable Splitting for Faster Non-Cartesian
-SPIRiT MR Image Reconstruction
Author :
Weller, Daniel S. ; Ramani, S. ; Fessler, Jeffrey A.
Author_Institution :
Dept. of Electr. Eng. & Comput. Sci., Univ. of Michigan, Ann Arbor, MI, USA
Abstract :
SPIRiT (iterative self-consistent parallel imaging reconstruction), and its sparsity-regularized variant L1-SPIRiT, are compatible with both Cartesian and non-Cartesian magnetic resonance imaging sampling trajectories. However, the non-Cartesian framework is more expensive computationally, involving a nonuniform Fourier transform with a nontrivial Gram matrix. We propose a novel implementation of the regularized reconstruction problem using variable splitting, alternating minimization of the augmented Lagrangian, and careful preconditioning. Our new method based on the alternating direction method of multipliers converges much faster than existing methods because of the preconditioners´ heightened effectiveness. We demonstrate such rapid convergence substantially improves image quality for a fixed computation time. Our framework is a step forward towards rapid non-Cartesian L1-SPIRiT reconstructions.
Keywords :
Fourier transforms; biomedical MRI; image reconstruction; iterative methods; medical image processing; minimisation; alternating direction method; alternating minimization; augmented Lagrangian; faster nonCartesian L1-SPIRiT magnetic resonance image reconstruction; fixed computation time; image quality; iterative self-consistent parallel imaging reconstruction; multipliers; nonCartesian magnetic resonance imaging sampling trajectories; nontrivial Gram matrix; nonuniform Fourier transform; rapid convergence; regularized reconstruction problem; sparsity-regularized variant L1 -SPIRiT; variable splitting; Coils; Convergence; Image reconstruction; Imaging; Mathematical model; Transforms; Tuning; Augmented Lagrangian; compressed sensing; magnetic resonance imaging (MRI); non-Cartesian reconstruction; parallel imaging reconstruction; preconditioning;
Journal_Title :
Medical Imaging, IEEE Transactions on
DOI :
10.1109/TMI.2013.2285046