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Parallel MR image reconstruction using augmented Lagrangian methods.

Sathish Ramani1, Jeffrey A Fessler

  • 1Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, MI 48109, USA. sramani@umich.edu

IEEE Transactions on Medical Imaging
|November 25, 2010
PubMed
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Novel augmented Lagrangian (AL) methods accelerate Magnetic Resonance Image (MRI) reconstruction using SENSitivity Encoding (SENSE). These faster algorithms improve image quality by efficiently handling regularization for undersampled data.

Area of Science:

  • Medical Imaging
  • Computational Science
  • Optimization Theory

Background:

  • Magnetic Resonance Image (MRI) reconstruction with SENSitivity Encoding (SENSE) requires regularization to mitigate noise and aliasing.
  • Current edge-preserving and sparsity-based regularization methods are effective but computationally demanding due to nonlinear optimization.
  • Efficient and faster reconstruction methods are crucial for advanced MRI applications.

Purpose of the Study:

  • To introduce novel augmented Lagrangian (AL) based methods for regularized MRI reconstruction from undersampled SENSE data.
  • To develop algorithms that efficiently solve the constrained optimization problems arising in SENSE reconstruction.
  • To demonstrate the applicability of these methods to a wide range of regularizers.

Main Methods:

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  • Formulation of regularized SENSE reconstruction as an unconstrained optimization problem.
  • Conversion to equivalent constrained problems using variable splitting.
  • Application of an alternating minimization method within the augmented Lagrangian framework.

Main Results:

  • The proposed AL algorithms are easily implementable and applicable to various regularizers, including total-variation and l(1)-norm wavelet coefficients.
  • Numerical experiments show faster convergence compared to nonlinear conjugate gradient (NCG) and MFISTA.
  • Successful reconstruction of both synthetic and in vivo human MRI data.

Conclusions:

  • The developed augmented Lagrangian algorithms offer a significant improvement in computational efficiency for regularized SENSE MRI reconstruction.
  • These methods provide a robust and faster alternative for processing undersampled MRI data.
  • The approach facilitates the use of complex regularization techniques, enhancing MRI image quality.