SRE-CNN: A Spatiotemporal Rotation-Equivariant CNN for Cardiac Cine MR Imaging

Dynamic MR images possess various transformation symmetries,including the rotation symmetry of local features within the image and along the temporal dimension. Utilizing these symmetries as prior knowledge can facilitate dynamic MR imaging with high spatiotemporal resolution. Equivariant CNN is an effective tool to leverage the symmetry priors. However, current equivariant CNN methods fail to fully exploit these symmetry priors in dynamic MR imaging. In this work, we propose a novel framework of Spatiotemporal Rotation-Equivariant CNN (SRE-CNN), spanning from the underlying high-precision filter design to the construction of the temporal-equivariant convolutional module and imaging model, to fully harness the rotation symmetries inherent in dynamic MR images. The temporal-equivariant convolutional module enables exploitation the rotation symmetries in both spatial and temporal dimensions, while the high-precision convolutional filter, based on parametrization strategy, enhances the utilization of rotation symmetry of local features to improve the reconstruction of detailed anatomical structures. Experiments conducted on highly undersampled dynamic cardiac cine data (up to 20X) have demonstrated the superior performance of our proposed approach, both quantitatively and qualitatively.

LINEAR: Learning Implicit Neural Representation With Explicit Physical Priors for Accelerated Quantitative T1rho Mapping

Quantitative T1rho parameter mapping has shown promise in clinical and research studies. However, it suffers from long scan times. Deep learning-based techniques have been successfully applied in accelerated quantitative MR parameter mapping. However, most methods require fully-sampled training dataset, which is impractical in the clinic. In this study, a novel subject-specific unsupervised method based on the implicit neural representation is proposed to reconstruct images from highly undersampled k-space data and estimate parameter maps from reconstructions, which only takes spatiotemporal coordinates as the input. Specifically, the proposed method learned a implicit neural representation of the MR images driven by two explicit priors of images (or k-space data), including the low-rankness of Hankel matrix, and the self-consistency of k-space data. The ablation experiments show that the proposed method can characterize the physical priors of MR images well. Moreover,experimental results of retrospective and prospective data show that the proposed method outperforms the state-of-the-art methods in terms of supressing artifacts and achieving the lowest error.

Harnessing Natural Oscillations for High-Speed, Efficient Asymmetrical Locomotion in Quadrupedal Robots

This study explores the dynamics of asymmetrical bounding gaits in quadrupedal robots, focusing on the integration of torso pitching and hip motion to enhance speed and stability. Traditional control strategies often enforce a fixed posture, minimizing natural body movements to simplify the control problem. However, this approach may overlook the inherent dynamical advantages found in natural locomotion. By considering the robot as two interconnected segments, we concentrate on stance leg motion while allowing passive torso oscillation, drawing inspiration from natural dynamics and underactuated robotics principles. Our control scheme employs Linear Inverted Pendulum (LIP) and Spring-Loaded Inverted Pendulum (SLIP) models to govern front and rear leg movements independently. This approach has been validated through extensive simulations and hardware experiments, demonstrating successful high-speed locomotion with top speeds nearing 4 m/s and reduced ground reaction forces, indicating a more efficient gait. Furthermore, unlike conventional methods, our strategy leverages natural torso oscillations to aid leg circulation and stride length, aligning robot dynamics more closely with biological counterparts. Our findings suggest that embracing the natural dynamics of quadrupedal movement, particularly in asymmetrical gaits like bounding, can lead to more stable, efficient, and high-speed robotic locomotion. This investigation lays the groundwork for future studies on versatile and dynamic quadrupedal gaits and their potential applications in scenarios demanding rapid and effective locomotion.

Learning Stable and Passive Neural Differential Equations

In this paper, we introduce a novel class of neural differential equation, which are intrinsically Lyapunov stable, exponentially stable or passive. We take a recently proposed Polyak Lojasiewicz network (PLNet) as an Lyapunov function and then parameterize the vector field as the descent directions of the Lyapunov function. The resulting models have a same structure as the general Hamiltonian dynamics, where the Hamiltonian is lower- and upper-bounded by quadratic functions. Moreover, it is also positive definite w.r.t. either a known or learnable equilibrium. We illustrate the effectiveness of the proposed model on a damped double pendulum system.

Proximal Gradient Descent Unfolding Dense-spatial Spectral-attention Transformer for Compressive Spectral Imaging

The Coded Aperture Snapshot Spectral Compressive Imaging (CASSI) system modulates three-dimensional hyperspectral images into two-dimensional compressed images in a single exposure. Subsequently, three-dimensional hyperspectral images (HSI) can be reconstructed from the two-dimensional compressed measurements using reconstruction algorithms. Among these methods, deep unfolding techniques have demonstrated excellent performance, with RDLUF-MixS^2 achieving the best reconstruction results. However, RDLUF-MixS^2 requires extensive training time, taking approximately 14 days to train RDLUF-MixS^2-9stg on a single RTX 3090 GPU, making it computationally expensive. Furthermore, RDLUF-MixS^2 performs poorly on real data, resulting in significant artifacts in the reconstructed images. In this study, we introduce the Dense-spatial Spectral-attention Transformer (DST) into the Proximal Gradient Descent Unfolding Framework (PGDUF), creating a novel approach called Proximal Gradient Descent Unfolding Dense-spatial Spectral-attention Transformer (PGDUDST). Compared to RDLUF-MixS^2, PGDUDST not only surpasses the network reconstruction performance limit of RDLUF-MixS^2 but also achieves faster convergence. PGDUDST requires only 58% of the training time of RDLUF-MixS^2-9stg to achieve comparable reconstruction results. Additionally, PGDUDST significantly alleviates the artifact issues caused by RDLUF-MixS^2 in real experimental data, demonstrating superior performance and producing clearer reconstructed images.

Physics-Informed DeepMRI: Bridging the Gap from Heat Diffusion to k-Space Interpolation

In the field of parallel imaging (PI), alongside image-domain regularization methods, substantial research has been dedicated to exploring $k$-space interpolation. However, the interpretability of these methods remains an unresolved issue. Furthermore, these approaches currently face acceleration limitations that are comparable to those experienced by image-domain methods. In order to enhance interpretability and overcome the acceleration limitations, this paper introduces an interpretable framework that unifies both $k$-space interpolation techniques and image-domain methods, grounded in the physical principles of heat diffusion equations. Building upon this foundational framework, a novel $k$-space interpolation method is proposed. Specifically, we model the process of high-frequency information attenuation in $k$-space as a heat diffusion equation, while the effort to reconstruct high-frequency information from low-frequency regions can be conceptualized as a reverse heat equation. However, solving the reverse heat equation poses a challenging inverse problem. To tackle this challenge, we modify the heat equation to align with the principles of magnetic resonance PI physics and employ the score-based generative method to precisely execute the modified reverse heat diffusion. Finally, experimental validation conducted on publicly available datasets demonstrates the superiority of the proposed approach over traditional $k$-space interpolation methods, deep learning-based $k$-space interpolation methods, and conventional diffusion models in terms of reconstruction accuracy, particularly in high-frequency regions.

RobustNeuralNetworks.jl: a Package for Machine Learning and Data-Driven Control with Certified Robustness

Neural networks are typically sensitive to small input perturbations, leading to unexpected or brittle behaviour. We present RobustNeuralNetworks.jl: a Julia package for neural network models that are constructed to naturally satisfy a set of user-defined robustness constraints. The package is based on the recently proposed Recurrent Equilibrium Network (REN) and Lipschitz-Bounded Deep Network (LBDN) model classes, and is designed to interface directly with Julia's most widely-used machine learning package, Flux.jl. We discuss the theory behind our model parameterization, give an overview of the package, and provide a tutorial demonstrating its use in image classification, reinforcement learning, and nonlinear state-observer design.

Meta-Learning Enabled Score-Based Generative Model for 1.5T-Like Image Reconstruction from 0.5T MRI

Magnetic resonance imaging (MRI) is known to have reduced signal-to-noise ratios (SNR) at lower field strengths, leading to signal degradation when producing a low-field MRI image from a high-field one. Therefore, reconstructing a high-field-like image from a low-field MRI is a complex problem due to the ill-posed nature of the task. Additionally, obtaining paired low-field and high-field MR images is often not practical. We theoretically uncovered that the combination of these challenges renders conventional deep learning methods that directly learn the mapping from a low-field MR image to a high-field MR image unsuitable. To overcome these challenges, we introduce a novel meta-learning approach that employs a teacher-student mechanism. Firstly, an optimal-transport-driven teacher learns the degradation process from high-field to low-field MR images and generates pseudo-paired high-field and low-field MRI images. Then, a score-based student solves the inverse problem of reconstructing a high-field-like MR image from a low-field MRI within the framework of iterative regularization, by learning the joint distribution of pseudo-paired images to act as a regularizer. Experimental results on real low-field MRI data demonstrate that our proposed method outperforms state-of-the-art unpaired learning methods.

SPIRiT-Diffusion: Self-Consistency Driven Diffusion Model for Accelerated MRI

Diffusion models are a leading method for image generation and have been successfully applied in magnetic resonance imaging (MRI) reconstruction. Current diffusion-based reconstruction methods rely on coil sensitivity maps (CSM) to reconstruct multi-coil data. However, it is difficult to accurately estimate CSMs in practice use, resulting in degradation of the reconstruction quality. To address this issue, we propose a self-consistency-driven diffusion model inspired by the iterative self-consistent parallel imaging (SPIRiT), namely SPIRiT-Diffusion. Specifically, the iterative solver of the self-consistent term in SPIRiT is utilized to design a novel stochastic differential equation (SDE) for diffusion process. Then $\textit{k}$-space data can be interpolated directly during the reverse diffusion process, instead of using CSM to separate and combine individual coil images. This method indicates that the optimization model can be used to design SDE in diffusion models, driving the diffusion process strongly conforming with the physics involved in the optimization model, dubbed model-driven diffusion. The proposed SPIRiT-Diffusion method was evaluated on a 3D joint Intracranial and Carotid Vessel Wall imaging dataset. The results demonstrate that it outperforms the CSM-based reconstruction methods, and achieves high reconstruction quality at a high acceleration rate of 10.

Energetic Analysis on the Optimal Bounding Gaits of Quadrupedal Robots

It is often overlooked by roboticists when designing locomotion controllers for their legged machines, that energy consumption plays an important role in selecting the best gaits for locomotion at high speeds or over long distances. The purpose of this study is to examine four similar asymmetrical quadrupedal gaits that are frequently observed in legged animals in nature. To understand how a specific footfall pattern will change the energetics of a legged system, we first developed a full body model of a quadrupedal robot called A1. And for each gait we created a hybrid system with desired footfall sequence and rigid impacts. In order to find the most energy efficient gait, we used optimal control methods to formulate the problem as a trajectory optimization problem with proper constraints and objective function. This problem was implemented and solved in a nonlinear programming framework called FROST. Based on the optimized trajectories for each gait, we investigated the values of cost of transport and the work done by all joints. Moreover, we analyzed the exchange of angular momentum in different components of the system during the whole stride cycle. According to the simulation results, bounding with two flight phases is likely to be the most energy efficient gait for A1 across a wide range of speed.