## 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 language | English |
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Article number | 1736 |

Pages (from-to) | 1-15 |

Number of pages | 15 |

Journal | Applied Sciences |

Volume | 1 |

Issue number | 12 |

DOIs | |

Publication status | Published - 2019 |

## Keywords

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

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