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Updated: May 22, 2026

Shaping the Amplitude and Phase of Laser Beams by Using a Phase-only Spatial Light Modulator
Published on: January 28, 2019
Separate magnitude and phase regularization via compressed sensing
Feng Zhao1, Douglas C Noll, Jon-Fredrik Nielsen
1Biomedical Engineering Department, The University of Michigan, Ann Arbor, MI 48109, USA. zhaofll@umich.edu
Abstract:
Compressed sensing (CS) has been used for accelerating magnetic resonance imaging acquisitions, but its use in applications with rapid spatial phase variations is challenging, e.g., proton resonance frequency shift (PRF-shift) thermometry and velocity mapping. Previously, an iterative MRI reconstruction with separate magnitude and phase regularization was proposed for applications where magnitude and phase maps are both of interest, but it requires fully sampled data and unwrapped phase maps. In this paper, CS is combined into this framework to reconstruct magnitude and phase images accurately from undersampled data. Moreover, new phase regularization terms are proposed to accommodate phase wrapping and to reconstruct images with encoded phase variations, e.g., PRF-shift thermometry and velocity mapping. The proposed method is demonstrated with simulated thermometry data and in vivo velocity mapping data and compared to conventional phase corrected CS.
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