CGME for general-form regularization with an application to low-field MRI

M.L. de Leeuw den Bouter, M.B. van Gijzen, R.F. Remis

Research output: Book/ReportReportProfessional


We generalize the CGME (Conjugate Gradient Minimal Error) algo-rithm to the weighted and regularized least squares problem. Analysis ofthe convergence of generalized CGME and CGLS shows that CGMEcanbe expected to perform better for ill-conditioned regularization matrices.Two different types of regularization are considered: anℓ1penalty andanℓ2penalty. Theℓ1problem is solved using Iterative Reweighted LeastSquares, which leads to an ill-conditioned regularizationmatrix. The twomethods are applied in a low-field MRI framework. The MRI physics ina low-field scanner are simulated to generate a noisy signal.When anℓ1penalty is used and iterative reweighted least squares isemployed, GCGLS needs significantly more iterations to converge thanGCGME. GCGME has a regularizing effect that leads to fewer artifactsin our simulations. This effect seems to be stronger when a lower numberof CG iterations is used. These two observations indicate that GCGMEis a very promising alternative to GCGLS.

Original languageEnglish
Place of PublicationDelft
PublisherDelft University of Technology
Number of pages23
Publication statusPublished - 2018

Publication series

NameReports of the Delft Institute of Applied Mathematics
ISSN (Print)1389-6520


Dive into the research topics of 'CGME for general-form regularization with an application to low-field MRI'. Together they form a unique fingerprint.

Cite this