Fast image reconstruction with L2‐regularization

Abstract

Purpose We introduce L2-regularized reconstruction algorithms with closed-form solutions that achieve dramatic computational speed-up relative to state of the art L1- and L2-based iterative algorithms while maintaining similar image quality for various applications in MRI reconstruction. Materials and Methods We compare fast L2-based methods to state of the art algorithms employing iterative L1- and L2-regularization in numerical phantom and in vivo data in three applications; 1) Fast Quantitative Susceptibility Mapping (QSD), 2) Lipid artifact suppression in Magnetic Resonance Spectroscopic Imaging (MRSI), and 3) Diffusion Spectrum Imaging (DSI). In all cases, proposed L2-based methods are compared with the state of the art algorithms, and two to three orders of magnitude speed up is demonstrated with similar reconstruction quality. Results The closed-form solution developed for regularized QSM allows processing of a 3D volume under 5 seconds, the proposed lipid suppression algorithm takes under 1 second to reconstruct single-slice MRSI data, while the PCA based DSI algorithm estimates diffusion propagators from undersampled q-space for a single slice under 30 seconds, all running in Matlab using a standard workstation. Conclusion For the applications considered herein, closed-form L2-regularization can be a faster alternative to its iterative counterpart or L1-based iterative algorithms, without compromising image quality.

A modulated closed form solution for quantitative susceptibility mapping — A thorough evaluation and comparison to iterative methods based on edge prior knowledge

“…The modulated closed form method has reconstruction errors smaller than those obtained both with similar direct methods proposed by other groups (Bilgic et al, 2013;Schweser et al, 2013). Not surprisingly, the optimum results (and independence on the regularization parameters) are found when the regularization is limited to a region tightly positioned around the magic angle cones (nthr = 0.1-0.2) as done in other k-space modulated iterative methods Wu et al, 2012).…”

“…The prior information is extracted from the phase and magnitude maps assuming them to have similar edges of the underlying brain structure or simply assuming that natural images are sparse in some basis set. Recently, it was noted that this could be performed as a direct inversion when assuming smoothness of the susceptibility map (Bilgic et al, 2013) (see Modulated closed form solution).…”

“…The prior information is extracted from the phase and magnitude maps assuming them to have similar edges of the underlying brain structure or simply assuming that natural images are sparse in some basis set. Recently, it was noted that this could be performed as a direct inversion when assuming smoothness of the susceptibility map (Bilgic et al, 2013) (see Modulated closed form solution).The aim of the present study was to perform a thorough comparison of some of these methods Liu et al, 2009; T. Liu et al, 2011) and a newly proposed methodology dubbed modulated closed form (MCF) both in simulations and in in-vivo data. Particularly we accurately evaluate the impact of the prior information and of the regularization parameters and how their optimality can be evaluated in the absence of ground truth.…”

Quantitative Susceptibility Mapping of Human Brain at 3T: A Multisite Reproducibility Study

“…23 Similar to the iterative QSM, the deterministic QSM involves minimization of the following equation:…”

Density‐weighted concentric circle trajectories for high resolution brain magnetic resonance spectroscopic imaging at 7T

“…Both, increased spatial resolution and spectral bandwidth, lead to increased demands on gradient systems and ultimately lower signal‐to‐noise ratio (SNR) efficiency 16, 17. Parallel imaging, on the other hand, becomes more efficient at higher B 0 , but achievable accelerations are lower than for SSE ( $\le 10$) 15 and lipid contamination is aggravated, which calls for additional lipid suppression techniques 2, 18, 19. While established SSE trajectories (i.e., EPSI, spirals) can be certainly optimized for higher B 0 , the increased gradient demands at 7T due to the increased spectral bandwidth make these trajectories inefficient for high spatial resolutions.…”