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Parallel MR image reconstruction using augmented Lagrangian methods.

ABSTRACT: 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.

SUBMITTER: Ramani S

PROVIDER: S-EPMC3081617 | biostudies-literature | 2011 Mar

REPOSITORIES: biostudies-literature

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Parallel MR image reconstruction using augmented Lagrangian methods.

Ramani Sathish S Fessler Jeffrey A JA

IEEE transactions on medical imaging 20101118 3

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-sc ...[more]

PMID: 21095861

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Project description:PURPOSE:Numerous image reconstruction methodologies for positron emission tomography (PET) have been developed that incorporate magnetic resonance (MR) imaging structural information, producing reconstructed images with improved suppression of noise and reduced partial volume effects. However, the influence of MR structural information also increases the possibility of suppression or bias of structures present only in the PET data (PET-unique regions). To address this, further developments for MR-informed methods have been proposed, for example, through inclusion of the current reconstructed PET image, alongside the MR image, in the iterative reconstruction process. In this present work, a number of kernel and maximum a posteriori (MAP) methodologies are compared, with the aim of identifying methods that enable a favorable trade-off between the suppression of noise and the retention of unique features present in the PET data. METHODS:The reconstruction methods investigated were: the MR-informed conventional and spatially compact kernel methods, referred to as KEM and KEM largest value sparsification (LVS) respectively; the MR-informed Bowsher and Gaussian MR-guided MAP methods; and the PET-MR-informed hybrid kernel and anato-functional MAP methods. The trade-off between improving the reconstruction of the whole brain region and the PET-unique regions was investigated for all methods in comparison with postsmoothed maximum likelihood expectation maximization (MLEM), evaluated in terms of structural similarity index (SSIM), normalized root mean square error (NRMSE), bias, and standard deviation. Both simulated BrainWeb (10 noise realizations) and real [18 F] fluorodeoxyglucose (FDG) three-dimensional datasets were used. The real [18 F]FDG dataset was augmented with simulated tumors to allow comparison of the reconstruction methodologies for the case of known regions of PET-MR discrepancy and evaluated at full counts (100%) and at a reduced (10%) count level. RESULTS:For the high-count simulated and real data studies, the anato-functional MAP method performed better than the other methods under investigation (MR-informed, PET-MR-informed and postsmoothed MLEM), in terms of achieving the best trade-off for the reconstruction of the whole brain and PET-unique regions, assessed in terms of the SSIM, NRMSE, and bias vs standard deviation. The inclusion of PET information in the anato-functional MAP method enables the reconstruction of PET-unique regions to attain similarly low levels of bias as unsmoothed MLEM, while moderately improving the whole brain image quality for low levels of regularization. However, for low count simulated datasets the anato-functional MAP method performs poorly, due to the inclusion of noisy PET information in the regularization term. For the low counts simulated dataset, KEM LVS and to a lesser extent, HKEM performed better than the other methods under investigation in terms of achieving the best trade-off for the reconstruction of the whole brain and PET-unique regions, assessed in terms of the SSIM, NRMSE, and bias vs standard deviation. CONCLUSION:For the reconstruction of noisy data, multiple MR-informed methods produce favorable whole brain vs PET-unique region trade-off in terms of the image quality metrics of SSIM and NRMSE, comfortably outperforming the whole image denoising of postsmoothed MLEM.

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Parallel MR image reconstruction using augmented Lagrangian methods.

Publications

Parallel MR image reconstruction using augmented Lagrangian methods.

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