Latent signal models: Learning compact representations of signal evolution for improved time‐resolved, multi‐contrast MRI

Abstract

Purpose: To improve time-resolved reconstructions by training auto-encoders to learn compact representations of Bloch-simulated signal evolution and inserting the decoder into the forward model. Methods: Building on model-based nonlinear and linear subspace techniques, we train auto-encoders on dictionaries of simulated signal evolution to learn compact, nonlinear, latent representations. The proposed latent signal model framework inserts the decoder portion of the auto-encoder into the forward model and directly reconstructs the latent representation. Latent signal models essentially serve as a proxy for fast and feasible differentiation through the Bloch equations used to simulate signal. This work performs experiments in the context of T 2 -shuffling, gradient echo EPTI, and MPRAGE-shuffling. We compare how efficiently auto-encoders represent signal evolution in comparison to linear subspaces. Simulation and in vivo experiments then evaluate if reducing degrees of freedom by incorporating our proxy for the Bloch equations, the decoder portion of the auto-encoder, into the forward model improves reconstructions in comparison to subspace constraints.Results: An auto-encoder with 1 real latent variable represents single-tissue fast spin echo, EPTI, and MPRAGE signal evolution to within 0.15% normalized RMS error, enabling reconstruction problems with 3 degrees of freedom per voxel (real latent variable + complex scaling) in comparison to linear models with 4-8 degrees of freedom per voxel. In simulated/in vivo T 2 -shuffling and in vivo EPTI experiments, the proposed framework achieves consistent quantitative normalized RMS error improvement over linear approaches. From qualitative evaluation, the proposed approach yields images with reduced blurring and noise amplification in MPRAGE-shuffling experiments. Conclusion:Directly solving for nonlinear latent representations of signal evolution improves time-resolved MRI reconstructions.

Single-shot Echo Planar Time-resolved Imaging for multi-echo functional MRI and distortion-free diffusion imaging

“…In this study, although single-shot EPTI was tested across a range of spatial resolution (e.g., 1.25 mm to 3 mm), further increasing spatial resolution (e.g., submillimeter resolution) will lead to higher undersampling in k-t space and may result in amplified noise or artifacts in the reconstructed images. Improved B 0 shimming (83)(84)(85) and hardware advancements such as high-performance gradient coils (e.g., head-only gradient coils (86-88)), and/or advanced reconstruction such as deep-learning-based approaches (89)(90)(91), can further improve reconstruction conditioning and achieve higher spatial resolution using ss-EPTI. Moreover, the temporal resolution of ss-EPTI can also be further improved.…”

Ultra-high temporal resolution 4D angiography using arterial spin labeling with subspace reconstruction

“…In some extreme cases, where transit time was short or dispersion sharpness was large, the signal variation could not be represented accurately by the compressed subspace, contributing to errors in the reconstructed images. Non-linear methods like autoencoders 38 are capable of representing complex signal variations with a smaller number of independent components (i.e., in the latent space), as demonstrated by Arefeen, et al 39 . However, the computational convenience brought by the permutation of linear operators would be lost, and the optimization would need to be performed with a subset of frames per iteration to accommodate limited memory.…”