Conjugate gradient variants for ℓ p -regularized image reconstruction in low-field MRI

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Abstract

We consider the MRI physics in a low-field MRI scanner, in which permanent magnets are used to generate a magnetic field in the millitesla range. A model describing the relationship between measured signal and image is derived, resulting in an ill-posed inverse problem. In order to solve it, a regularization penalty is added to the least-squares minimization problem. We generalize the conjugate gradient minimal error (CGME) algorithm to the weighted and regularized least-squares problem. Analysis of the convergence of generalized CGME (GCGME) and the classical generalized conjugate gradient least squares (GCGLS) shows that GCGME can be expected to converge faster for ill-conditioned regularization matrices. The ℓ p-regularized problem is solved using iterative reweighted least squares for p= 1 and p=12, with both cases leading to an increasingly ill-conditioned regularization matrix. Numerical results show that GCGME needs a significantly lower number of iterations to converge than GCGLS.

Original languageEnglish
Article number1736
Pages (from-to)1-15
Number of pages15
JournalApplied Sciences
Volume1
Issue number12
DOIs
Publication statusPublished - 2019

Keywords

  • Conjugate gradient method
  • Halbach cylinder
  • Image reconstruction
  • Iterative reweighted least squares
  • Low-field MRI
  • Magnetic resonance imaging
  • Regularization

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