High-Dimensional Sparse Bayesian Learning without Covariance Matrices

Sparse Bayesian learning (SBL) is a powerful framework for tackling the sparse coding problem. However, the most popular inference algorithms for SBL become too expensive for high-dimensional settings, due to the need to store and compute a large covariance matrix. We introduce a new inference scheme that avoids explicit construction of the covariance matrix by solving multiple linear systems in parallel to obtain the posterior moments for SBL. Our approach couples a little-known diagonal estimation result from numerical linear algebra with the conjugate gradient algorithm. On several simulations, our method scales better than existing approaches in computation time and memory, especially for structured dictionaries capable of fast matrix-vector multiplication.

Wave-Encoded Model-based Deep Learning for Highly Accelerated Imaging with Joint Reconstruction

Purpose: To propose a wave-encoded model-based deep learning (wave-MoDL) strategy for highly accelerated 3D imaging and joint multi-contrast image reconstruction, and further extend this to enable rapid quantitative imaging using an interleaved look-locker acquisition sequence with T2 preparation pulse (3D-QALAS). Method: Recently introduced MoDL technique successfully incorporates convolutional neural network (CNN)-based regularizers into physics-based parallel imaging reconstruction using a small number of network parameters. Wave-CAIPI is an emerging parallel imaging method that accelerates the imaging speed by employing sinusoidal gradients in the phase- and slice-encoding directions during the readout to take better advantage of 3D coil sensitivity profiles. In wave-MoDL, we propose to combine the wave-encoding strategy with unrolled network constraints to accelerate the acquisition speed while enforcing wave-encoded data consistency. We further extend wave-MoDL to reconstruct multi-contrast data with controlled aliasing in parallel imaging (CAIPI) sampling patterns to leverage similarity between multiple images to improve the reconstruction quality. Result: Wave-MoDL enables a 47-second MPRAGE acquisition at 1 mm resolution at 16-fold acceleration. For quantitative imaging, wave-MoDL permits a 2-minute acquisition for T1, T2, and proton density mapping at 1 mm resolution at 12-fold acceleration, from which contrast weighted images can be synthesized as well. Conclusion: Wave-MoDL allows rapid MR acquisition and high-fidelity image reconstruction and may facilitate clinical and neuroscientific applications by incorporating unrolled neural networks into wave-CAIPI reconstruction.

Accurate parameter estimation using scan-specific unsupervised deep learning for relaxometry and MR fingerprinting

We propose an unsupervised convolutional neural network (CNN) for relaxation parameter estimation. This network incorporates signal relaxation and Bloch simulations while taking advantage of residual learning and spatial relations across neighboring voxels. Quantification accuracy and robustness to noise is shown to be significantly improved compared to standard parameter estimation methods in numerical simulations and in vivo data for multi-echo T2 and T2* mapping. The combination of the proposed network with subspace modeling and MR fingerprinting (MRF) from highly undersampled data permits high quality T1 and T2 mapping.

Quantifying the uncertainty of neural networks using Monte Carlo dropout for deep learning based quantitative MRI

Dropout is conventionally used during the training phase as regularization method and for quantifying uncertainty in deep learning. We propose to use dropout during training as well as inference steps, and average multiple predictions to improve the accuracy, while reducing and quantifying the uncertainty. The results are evaluated for fractional anisotropy (FA) and mean diffusivity (MD) maps which are obtained from only 3 direction scans. With our method, accuracy can be improved significantly compared to network outputs without dropout, especially when the training dataset is small. Moreover, confidence maps are generated which may aid in diagnosis of unseen pathology or artifacts.

SDnDTI: Self-supervised deep learning-based denoising for diffusion tensor MRI

The noise in diffusion-weighted images (DWIs) decreases the accuracy and precision of diffusion tensor magnetic resonance imaging (DTI) derived microstructural parameters and leads to prolonged acquisition time for achieving improved signal-to-noise ratio (SNR). Deep learning-based image denoising using convolutional neural networks (CNNs) has superior performance but often requires additional high-SNR data for supervising the training of CNNs, which reduces the practical feasibility. We develop a self-supervised deep learning-based method entitled "SDnDTI" for denoising DTI data, which does not require additional high-SNR data for training. Specifically, SDnDTI divides multi-directional DTI data into many subsets, each consisting of six DWI volumes along optimally chosen diffusion-encoding directions that are robust to noise for the tensor fitting, and then synthesizes DWI volumes along all acquired directions from the diffusion tensors fitted using each subset of the data as the input data of CNNs. On the other hand, SDnDTI synthesizes DWI volumes along acquired diffusion-encoding directions with higher SNR from the diffusion tensors fitted using all acquired data as the training target. SDnDTI removes noise from each subset of synthesized DWI volumes using a deep 3-dimensional CNN to match the quality of the cleaner target DWI volumes and achieves even higher SNR by averaging all subsets of denoised data. The denoising efficacy of SDnDTI is demonstrated on two datasets provided by the Human Connectome Project (HCP) and the Lifespan HCP in Aging. The SDnDTI results preserve image sharpness and textural details and substantially improve upon those from the raw data. The results of SDnDTI are comparable to those from supervised learning-based denoising and outperform those from state-of-the-art conventional denoising algorithms including BM4D, AONLM and MPPCA.

BUDA-SAGE with self-supervised denoising enables fast, distortion-free, high-resolution T2, T2*, para- and dia-magnetic susceptibility mapping

To rapidly obtain high resolution T2, T2* and quantitative susceptibility mapping (QSM) source separation maps with whole-brain coverage and high geometric fidelity. We propose Blip Up-Down Acquisition for Spin And Gradient Echo imaging (BUDA-SAGE), an efficient echo-planar imaging (EPI) sequence for quantitative mapping. The acquisition includes multiple T2*-, T2'- and T2-weighted contrasts. We alternate the phase-encoding polarities across the interleaved shots in this multi-shot navigator-free acquisition. A field map estimated from interim reconstructions was incorporated into the joint multi-shot EPI reconstruction with a structured low rank constraint to eliminate geometric distortion. A self-supervised MR-Self2Self (MR-S2S) neural network (NN) was utilized to perform denoising after BUDA reconstruction to boost SNR. Employing Slider encoding allowed us to reach 1 mm isotropic resolution by performing super-resolution reconstruction on BUDA-SAGE volumes acquired with 2 mm slice thickness. Quantitative T2 and T2* maps were obtained using Bloch dictionary matching on the reconstructed echoes. QSM was estimated using nonlinear dipole inversion (NDI) on the gradient echoes. Starting from the estimated R2 and R2* maps, R2' information was derived and used in source separation QSM reconstruction, which provided additional para- and dia-magnetic susceptibility maps. In vivo results demonstrate the ability of BUDA-SAGE to provide whole-brain, distortion-free, high-resolution multi-contrast images and quantitative T2 and T2* maps, as well as yielding para- and dia-magnetic susceptibility maps. Derived quantitative maps showed comparable values to conventional mapping methods in phantom and in vivo measurements. BUDA-SAGE acquisition with self-supervised denoising and Slider encoding enabled rapid, distortion-free, whole-brain T2, T2* mapping at 1 mm3 isotropic resolution in 90 seconds.

Optimized multi-axis spiral projection MR fingerprinting with subspace reconstruction for rapid whole-brain high-isotropic-resolution quantitative imaging

Purpose: To improve image quality and accelerate the acquisition of 3D MRF. Methods: Building on the multi-axis spiral-projection MRF technique, a subspace reconstruction with locally low rank (LLR) constraint and a modified spiral-projection spatiotemporal encoding scheme termed tiny-golden-angle-shuffling (TGAS) were implemented for rapid whole-brain high-resolution quantitative mapping. The LLR regularization parameter and the number of subspace bases were tuned using retrospective in-vivo data and simulated examinations, respectively. B0 inhomogeneity correction using multi-frequency interpolation was incorporated into the subspace reconstruction to further improve the image quality by mitigating blurring caused by off-resonance effect. Results: The proposed MRF acquisition and reconstruction framework can produce provide high quality 1-mm isotropic whole-brain quantitative maps in a total acquisition time of 1 minute 55 seconds, with higher-quality results than ones obtained from the previous approach in 6 minutes. The comparison of quantitative results indicates that neither the subspace reconstruction nor the TGAS trajectory induce bias for T1 and T2 mapping. High quality whole-brain MRF data were also obtained at 0.66-mm isotropic resolution in 4 minutes using the proposed technique, where the increased resolution was shown to improve visualization of subtle brain structures. Conclusion: The proposed TGAS-SPI-MRF with optimized spiral-projection trajectory and subspace reconstruction can enable high-resolution quantitative mapping with faster acquisition speed.

eRAKI: Fast Robust Artificial neural networks for K-space Interpolation (RAKI) with Coil Combination and Joint Reconstruction

RAKI can perform database-free MRI reconstruction by training models using only auto-calibration signal (ACS) from each specific scan. As it trains a separate model for each individual coil, learning and inference with RAKI can be computationally prohibitive, particularly for large 3D datasets. In this abstract, we accelerate RAKI more than 200 times by directly learning a coil-combined target and further improve the reconstruction performance using joint reconstruction across multiple echoes together with an elliptical-CAIPI sampling approach. We further deploy these improvements in quantitative imaging and rapidly obtain T2 and T2* parameter maps from a fast EPTI scan.