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- W2990341765 abstract "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 $${ell}_{p}$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:msub><mml:mi>ℓ</mml:mi><mml:mi>p</mml:mi></mml:msub></mml:math> -regularized problem is solved using iterative reweighted least squares for $$p=1$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:mrow><mml:mi>p</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math> and $$p=frac{1}{2}$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:mrow><mml:mi>p</mml:mi><mml:mo>=</mml:mo><mml:mfrac><mml:mn>1</mml:mn><mml:mn>2</mml:mn></mml:mfrac></mml:mrow></mml:math> , 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." @default.
- W2990341765 created "2019-12-05" @default.
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- W2990341765 date "2019-11-30" @default.
- W2990341765 modified "2023-10-17" @default.
- W2990341765 title "Conjugate gradient variants for $${ell}_{p}$$-regularized image reconstruction in low-field MRI" @default.
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- W2990341765 doi "https://doi.org/10.1007/s42452-019-1670-2" @default.
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