Premium
MR image reconstruction from undersampled data by using the iterative refinement procedure
Author(s) -
He Lin,
Chang TiChiun,
Osher Stanley,
Fang Tong,
Speier Peter
Publication year - 2007
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200700776
Subject(s) - iterated function , regularization (linguistics) , iterative reconstruction , compressed sensing , norm (philosophy) , iterative method , inverse problem , wavelet , nonlinear system , computer science , algorithm , sparse approximation , mathematical optimization , scale space , mathematics , image (mathematics) , artificial intelligence , image processing , mathematical analysis , physics , quantum mechanics , political science , law
Magnetic resonance imaging (MRI) reconstruction from sparsely sampled data has been a difficult problem in medical imaging field. We approach this problem by formulating a cost functional that includes a constraint term that is imposed by the raw measurement data in k‐space and the L 1 norm of a sparse representation of the reconstructed image. The sparse representation is usually realized by total variational regularization and/or wavelet transform. We have applied the Bregman iteration to minimize this functional to recover finer scales in our recent work. Here we propose nonlinear inverse scale space methods in addition to the iterative refinement procedure. Numerical results from the two methods are presented and it shows that the nonlinear inverse scale space method is a more efficient algorithm than the iterated refinement method. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)