Low-Rank Modeling of Local k-Space Neighborhoods (LORAKS) for Constrained MRI

By Justin P. Haldar. IEEE Transactions on Medical Imaging, 2014

345 citations recorded by the source corpus.

Recent theoretical results on low-rank matrix reconstruction have inspired significant interest in low-rank modeling of MRI images. Existing approaches have focused on higher-dimensional scenarios with data available from multiple channels, timepoints, or image contrasts. The present work demonstrates that single-channel, single-contrast, single-timepoint k-space data can also be mapped to low-rank matrices when the image has limited spatial support or slowly varying phase. Based on this, we develop a novel and flexible framework for constrained image reconstruction that uses low-rank matrix modeling of local k-space neighborhoods (LORAKS). A new regularization penalty and corresponding algorithm for promoting low-rank are also introduced. The potential of LORAKS is demonstrated with simulated and experimental data for a range of denoising and sparse-sampling applications. LORAKS is also compared against state-of-the-art methods like homodyne reconstruction, l1-norm minimization, and total variation minimization, and is demonstrated to have distinct features and advantages. In addition, while calibration-based support and phase constraints are commonly used in existing methods, the LORAKS framework enables calibrationless use of these constraints.

Subfields: Computational Mechanics, Radiology, Nuclear Medicine and Imaging

View Paper: https://www.semanticscholar.org/paper/071732c06943df639108c162a020e7f81708a0e5

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In Computational Mechanics

In Radiology, Nuclear Medicine and Imaging

Citations in the corpus

Monarch: Expressive Structured Matrices for Efficient and Accurate Training (2022, methodology): “Low-rank methods enforce low rank structure across slowly-varying dimensions or local patches in the data (Ong & Lustig, 2016; Ravishankar et al., 2017; Haldar, 2013).”
Deep-Learning Methods for Parallel Magnetic Resonance Imaging Reconstruction: A Survey of the Current Approaches, Trends, and Issues (2019, methodology): “Low-rank matrix modeling of local k-space neighborhoods (LORAKS) is another method exploiting similar ideas, where the motivation is based on utilizing finite image support and image phase constraints instead of correlations across multiple coils [37].”
MoDL: Model-Based Deep Learning Architecture for Inverse Problems (2017, background): “Recently, several authors have also recently introduced structured low-rank based priors that encourage super-resolution image recovery [26], [29]–[31].”