Journal
IEEE TRANSACTIONS ON MEDICAL IMAGING
Volume 30, Issue 3, Pages 694-706Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TMI.2010.2093536
Keywords
Augmented Lagrangian; image reconstruction; parallel magnetic resonance imaging (MRI); regularization; sensitivity encoding (SENSE)
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Funding
- Swiss National Science Foundation [PBELP2-125446]
- National Institutes of Health [P01 CA87634]
- Swiss National Science Foundation (SNF) [PBELP2-125446] Funding Source: Swiss National Science Foundation (SNF)
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Magnetic resonance image (MRI) reconstruction using SENSitivity Encoding (SENSE) requires regularization to suppress noise and aliasing effects. Edge-preserving and sparsity-based regularization criteria can improve image quality, but they demand computation-intensive nonlinear optimization. In this paper, we present novel methods for regularized MRI reconstruction from undersampled sensitivity encoded data-SENSE-reconstruction-using the augmented Lagrangian (AL) framework for solving large-scale constrained optimization problems. We first formulate regularized SENSE-reconstruction as an unconstrained optimization task and then convert it to a set of (equivalent) constrained problems using variable splitting. We then attack these constrained versions in an AL framework using an alternating minimization method, leading to algorithms that can be implemented easily. The proposed methods are applicable to a general class of regularizers that includes popular edge-preserving (e.g., total-variation) and sparsity-promoting (e.g., l(1)-norm of wavelet coefficients) criteria and combinations thereof. Numerical experiments with synthetic and in vivo human data illustrate that the proposed AL algorithms converge faster than both general-purpose optimization algorithms such as nonlinear conjugate gradient (NCG) and state-of-the-art MFISTA.
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