Motion-Robust Deep Reconstruction for Free-Breathing Cardiac Cine MRI

Conventional cardiac cine MRI relies on breath-hold Cartesian acquisitions, which are vulnerable to motion artifacts and can be uncomfortable or infeasible, particularly for pediatric and other noncompliant patients who cannot reliably hold their breath. Free-breathing radial acquisitions can alleviate these limitations, but robust reconstruction at high acceleration remains challenging due to prominent streak artifacts. To address these limitations, we propose Cine-DL, a clinically oriented framework that couples targeted k-space preprocessing with fast, model-based deep reconstruction. In this pipeline, raw free-breathing radial data undergo retrospective cardiac binning and respiratory gating to resolve cardiac phases and discard motion-corrupted spokes. We then introduce Streak Optimized Coil Compression (SOC), which explicitly preserves cardiac signals while suppressing peripheral interference that typically drives the streak artifacts. The resulting 2D+t cine series is reconstructed with an unrolled network that alternates a ResNet proximal operator with physics-based data consistency updates solved via conjugate gradient. We further employ a memory-efficient training strategy that reduces peak memory usage. We evaluate Cine-DL on free-breathing volunteer data against established baselines (k-t SENSE and iGRASP) and demonstrate clinical translation via hospital deployment on newly acquired patient data. Our experiments show that Cine-DL consistently improves quantitative metrics and visual fidelity, supporting a practical route toward routine, time-sensitive clinical adoption of free-breathing cine MRI.

Quantitative Approximation Rates for Group Equivariant Learning

The universal approximation theorem establishes that neural networks can approximate any continuous function on a compact set. Later works in approximation theory provide quantitative approximation rates for ReLU networks on the class of $α$-Hölder functions $f: [0,1]^N \to \mathbb{R}$. The goal of this paper is to provide similar quantitative approximation results in the context of group equivariant learning, where the learned $α$-Hölder function is known to obey certain group symmetries. While there has been much interest in the literature in understanding the universal approximation properties of equivariant models, very few quantitative approximation results are known for equivariant models. In this paper, we bridge this gap by deriving quantitative approximation rates for several prominent group-equivariant and invariant architectures. The architectures that we consider include: the permutation-invariant Deep Sets architecture; the permutation-equivariant Sumformer and Transformer architectures; joint invariance to permutations and rigid motions using invariant networks based on frame averaging; and general bi-Lipschitz invariant models. Overall, we show that equally-sized ReLU MLPs and equivariant architectures are equally expressive over equivariant functions. Thus, hard-coding equivariance does not result in a loss of expressivity or approximation power in these models.

In-Context Multi-Operator Learning with DeepOSets

In-context Learning (ICL) is the remarkable capability displayed by some machine learning models to learn from examples in a prompt, without any further weight updates. ICL had originally been thought to emerge from the self-attention mechanism in autoregressive transformer architectures. DeepOSets is a non-autoregressive, non-attention based neural architecture that combines set learning via the DeepSets architecture with operator learning via Deep Operator Networks (DeepONets). In a previous study, DeepOSets was shown to display ICL capabilities in supervised learning problems. In this paper, we show that the DeepOSets architecture, with the appropriate modifications, is a multi-operator in-context learner that can recover the solution operator of a new PDE, not seen during training, from example pairs of parameter and solution placed in a user prompt, without any weight updates. Furthermore, we show that DeepOSets is a universal uniform approximator over a class of continuous operators, which we believe is the first result of its kind in the literature of scientific machine learning. This means that a single DeepOSets architecture exists that approximates in-context any continuous operator in the class to any fixed desired degree accuracy, given an appropriate number of examples in the prompt. Experiments with Poisson and reaction-diffusion forward and inverse boundary-value problems demonstrate the ability of the proposed model to use in-context examples to predict accurately the solutions corresponding to parameter queries for PDEs not seen during training.