Non-Cartesian MRI Reconstruction With Automatic Regularization Via Monte-Carlo SURE

• Published in: IEEE transactions on medical imaging Vol. 32; no. 8; pp. 1411 - 1422
• Main Authors: Ramani, Sathish, Weller, Daniel S., Nielsen, Jon-Fredrik, Fessler, Jeffrey A.
• Format: Journal Article
• Language: English
• Published: United States IEEE 01.08.2013
• Subjects: Algorithms; Computer Simulation; Data models; Humans; Image Processing, Computer-Assisted - methods; Image reconstruction; Magnetic resonance imaging; Magnetic Resonance Imaging - methods; Monte Carlo Method; Monte Carlo methods; non-Cartesian MRI; Phantoms, Imaging; Reconstruction algorithms; regularization parameter; Stein's unbiased risk estimate (SURE); Vectors
• ISSN: 0278-0062; 1558-254X; 1558-254X
• DOI: 10.1109/TMI.2013.2257829

Magnetic resonance image (MRI) reconstruction from undersampled k-space data requires regularization to reduce noise and aliasing artifacts. Proper application of regularization however requires appropriate selection of associated regularization parameters. In this work, we develop a data-driven regularization parameter adjustment scheme that minimizes an estimate [based on the principle of Stein's unbiased risk estimate (SURE)] of a suitable weighted squared-error measure in k-space. To compute this SURE-type estimate, we propose a Monte-Carlo scheme that extends our previous approach to inverse problems (e.g., MRI reconstruction) involving complex-valued images. Our approach depends only on the output of a given reconstruction algorithm and does not require knowledge of its internal workings, so it is capable of tackling a wide variety of reconstruction algorithms and nonquadratic regularizers including total variation and those based on the l 1 -norm. Experiments with simulated and real MR data indicate that the proposed approach is capable of providing near mean squared-error optimal regularization parameters for single-coil undersampled non-Cartesian MRI reconstruction.