Non-Uniform Sampling Reconstruction for Symmetrical NMR Spectroscopy by Exploiting Inherent Symmetry

Symmetrical NMR spectroscopy constitutes a vital branch of multidimensional NMR spectroscopy, providing a powerful tool for the structural elucidation of biological macromolecules. Non-Uniform Sampling (NUS) serves as an effective strategy for averting the prohibitive acquisition time of multidimensional NMR spectroscopy by only sampling a few points according to NUS sampling schedules and reconstructing missing points via algorithms. However, current sampling schedules are unable to maintain the accurate recovery of cross peaks that are weak but important. In this work, we propose a novel sampling schedule termed as SCPG (Symmetrical Copy Poisson Gap) and employ CS (Compressed Sensing) methods for reconstruction. We theoretically prove that the symmetrical constraint, apart from sparsity, is implicitly implemented when SCPG is combined with CS methods. The simulated and experimental data substantiate the advantage of SCPG over state-of-the-art 2D Woven PG in the NUS reconstruction of symmetrical NMR spectroscopy.

High-efficient deep learning-based DTI reconstruction with flexible diffusion gradient encoding scheme

Purpose: To develop and evaluate a novel dynamic-convolution-based method called FlexDTI for high-efficient diffusion tensor reconstruction with flexible diffusion encoding gradient schemes. Methods: FlexDTI was developed to achieve high-quality DTI parametric mapping with flexible number and directions of diffusion encoding gradients. The proposed method used dynamic convolution kernels to embed diffusion gradient direction information into feature maps of the corresponding diffusion signal. Besides, our method realized the generalization of a flexible number of diffusion gradient directions by setting the maximum number of input channels of the network. The network was trained and tested using data sets from the Human Connectome Project and a local hospital. Results from FlexDTI and other advanced tensor parameter estimation methods were compared. Results: Compared to other methods, FlexDTI successfully achieves high-quality diffusion tensor-derived variables even if the number and directions of diffusion encoding gradients are variable. It increases peak signal-to-noise ratio (PSNR) by about 10 dB on Fractional Anisotropy (FA) and Mean Diffusivity (MD), compared with the state-of-the-art deep learning method with flexible diffusion encoding gradient schemes. Conclusion: FlexDTI can well learn diffusion gradient direction information to achieve generalized DTI reconstruction with flexible diffusion gradient schemes. Both flexibility and reconstruction quality can be taken into account in this network.

One for Multiple: Physics-informed Synthetic Data Boosts Generalizable Deep Learning for Fast MRI Reconstruction

Magnetic resonance imaging (MRI) is a principal radiological modality that provides radiation-free, abundant, and diverse information about the whole human body for medical diagnosis, but suffers from prolonged scan time. The scan time can be significantly reduced through k-space undersampling but the introduced artifacts need to be removed in image reconstruction. Although deep learning (DL) has emerged as a powerful tool for image reconstruction in fast MRI, its potential in multiple imaging scenarios remains largely untapped. This is because not only collecting large-scale and diverse realistic training data is generally costly and privacy-restricted, but also existing DL methods are hard to handle the practically inevitable mismatch between training and target data. Here, we present a Physics-Informed Synthetic data learning framework for Fast MRI, called PISF, which is the first to enable generalizable DL for multi-scenario MRI reconstruction using solely one trained model. For a 2D image, the reconstruction is separated into many 1D basic problems and starts with the 1D data synthesis, to facilitate generalization. We demonstrate that training DL models on synthetic data, integrated with enhanced learning techniques, can achieve comparable or even better in vivo MRI reconstruction compared to models trained on a matched realistic dataset, reducing the demand for real-world MRI data by up to 96%. Moreover, our PISF shows impressive generalizability in multi-vendor multi-center imaging. Its excellent adaptability to patients has been verified through 10 experienced doctors' evaluations. PISF provides a feasible and cost-effective way to markedly boost the widespread usage of DL in various fast MRI applications, while freeing from the intractable ethical and practical considerations of in vivo human data acquisitions.

Convex Dual Theory Analysis of Two-Layer Convolutional Neural Networks with Soft-Thresholding

Soft-thresholding has been widely used in neural networks. Its basic network structure is a two-layer convolution neural network with soft-thresholding. Due to the network's nature of nonlinearity and nonconvexity, the training process heavily depends on an appropriate initialization of network parameters, resulting in the difficulty of obtaining a globally optimal solution. To address this issue, a convex dual network is designed here. We theoretically analyze the network convexity and numerically confirm that the strong duality holds. This conclusion is further verified in the linear fitting and denoising experiments. This work provides a new way to convexify soft-thresholding neural networks.

Model-based Synthetic Data-driven Learning (MOST-DL): Application in Single-shot T2 Mapping with Severe Head Motion Using Overlapping-echo Acquisition

Data-driven learning algorithm has been successfully applied to facilitate reconstruction of medical imaging. However, real-world data needed for supervised learning are typically unavailable or insufficient, especially in the field of magnetic resonance imaging (MRI). Synthetic training samples have provided a potential solution for such problem, while the challenge brought by various non-ideal situations were usually encountered especially under complex experimental conditions. In this study, a general framework, Model-based Synthetic Data-driven Learning (MOST-DL), was proposed to generate paring data for network training to achieve robust T2 mapping using overlapping-echo acquisition under severe head motion accompanied with inhomogeneous RF field. We decomposed this challenging task into parallel reconstruction and motion correction according to a forward model. The neural network was first trained in pure synthetic dataset and then evaluated with in vivo human brain. Experiments showed that MOST-DL method significantly reduces ghosting and motion artifacts in T2 maps in the presence of random and continuous subject movement. We believe that the proposed approach may open a door for solving similar problems with other MRI acquisition methods and can be extended to other areas of medical imaging.

Fed-EINI: An Efficient and Interpretable Inference Framework for Decision Tree Ensembles in Federated Learning

The increasing concerns about data privacy and security drives the emergence of a new field of studying privacy-preserving machine learning from isolated data sources, i.e., \textit{federated learning}. Vertical federated learning, where different parties hold different features for common users, has a great potential of driving a more variety of business cooperation among enterprises in different fields. Decision tree models especially decision tree ensembles are a class of widely applied powerful machine learning models with high interpretability and modeling efficiency. However, the interpretability are compromised in these works such as SecureBoost since the feature names are not exposed to avoid possible data breaches due to the unprotected decision path. In this paper, we shall propose Fed-EINI, an efficient and interpretable inference framework for federated decision tree models with only one round of multi-party communication. We shall compute the candidate sets of leaf nodes based on the local data at each party in parallel, followed by securely computing the weight of the only leaf node in the intersection of the candidate sets. We propose to protect the decision path by the efficient additively homomorphic encryption method, which allows the disclosure of feature names and thus makes the federated decision trees interpretable. The advantages of Fed-EINI will be demonstrated through theoretical analysis and extensive numerical results. Experiments show that the inference efficiency is improved by over $50\%$ in average.

Accelerated Nuclear Magnetic Resonance Spectroscopy with Deep Learning

Nuclear magnetic resonance (NMR) spectroscopy serves as an indispensable tool in chemistry and biology but often suffers from long experimental time. We present a proof-of-concept of application of deep learning and neural network for high-quality, reliable, and very fast NMR spectra reconstruction from limited experimental data. We show that the neural network training can be achieved using solely synthetic NMR signal, which lifts the prohibiting demand for a large volume of realistic training data usually required in the deep learning approach.

High Efficient Reconstruction of Single-shot T2 Mapping from OverLapping-Echo Detachment Planar Imaging Based on Deep Residual Network

Purpose: An end-to-end deep convolutional neural network (CNN) based on deep residual network (ResNet) was proposed to efficiently reconstruct reliable T2 mapping from single-shot OverLapping-Echo Detachment (OLED) planar imaging. Methods: The training dataset was obtained from simulations carried out on SPROM software developed by our group. The relationship between the original OLED image containing two echo signals and the corresponded T2 mapping was learned by ResNet training. After the ResNet was trained, it was applied to reconstruct the T2 mapping from simulation and in vivo human brain data. Results: Though the ResNet was trained entirely on simulated data, the trained network was generalized well to real human brain data. The results from simulation and in vivo human brain experiments show that the proposed method significantly outperformed the echo-detachment-based method. Reliable T2 mapping was achieved within tens of milliseconds after the network had been trained while the echo-detachment-based OLED reconstruction method took minutes. Conclusion: The proposed method will greatly facilitate real-time dynamic and quantitative MR imaging via OLED sequence, and ResNet has the potential to reconstruct images from complex MRI sequence efficiently.

Hankel Matrix Nuclear Norm Regularized Tensor Completion for $N$-dimensional Exponential Signals

Signals are generally modeled as a superposition of exponential functions in spectroscopy of chemistry, biology and medical imaging. For fast data acquisition or other inevitable reasons, however, only a small amount of samples may be acquired and thus how to recover the full signal becomes an active research topic. But existing approaches can not efficiently recover $N$-dimensional exponential signals with $N\geq 3$. In this paper, we study the problem of recovering N-dimensional (particularly $N\geq 3$) exponential signals from partial observations, and formulate this problem as a low-rank tensor completion problem with exponential factor vectors. The full signal is reconstructed by simultaneously exploiting the CANDECOMP/PARAFAC structure and the exponential structure of the associated factor vectors. The latter is promoted by minimizing an objective function involving the nuclear norm of Hankel matrices. Experimental results on simulated and real magnetic resonance spectroscopy data show that the proposed approach can successfully recover full signals from very limited samples and is robust to the estimated tensor rank.

Fast Multi-class Dictionaries Learning with Geometrical Directions in MRI Reconstruction

Objective: Improve the reconstructed image with fast and multi-class dictionaries learning when magnetic resonance imaging is accelerated by undersampling the k-space data. Methods: A fast orthogonal dictionary learning method is introduced into magnetic resonance image reconstruction to providing adaptive sparse representation of images. To enhance the sparsity, image is divided into classified patches according to the same geometrical direction and dictionary is trained within each class. A new sparse reconstruction model with the multi-class dictionaries is proposed and solved using a fast alternating direction method of multipliers. Results: Experiments on phantom and brain imaging data with acceleration factor up to 10 and various undersampling patterns are conducted. The proposed method is compared with state-of-the-art magnetic resonance image reconstruction methods. Conclusion: Artifacts are better suppressed and image edges are better preserved than the compared methods. Besides, the computation of the proposed approach is much faster than the typical K-SVD dictionary learning method in magnetic resonance image reconstruction. Significance: The proposed method can be exploited in undersapmled magnetic resonance imaging to reduce data acquisition time and reconstruct images with better image quality.