Abstract
Recovering high-fidelity 3D images from sparse or degraded 2D images is a fundamental challenge in medical imaging, with broad applications ranging from 3D ultrasound reconstruction to MRI super-resolution. In the context of fetal MRI, high-resolution 3D reconstruction of the brain from motion-corrupted low-resolution 2D acquisitions is a prerequisite for accurate neurodevelopmental diagnosis. While implicit neural representations (INRs) have recently established state-of-the-art performance in self-supervised slice-to-volume reconstruction (SVR), they suffer from a critical computational bottleneck: accurately modeling the image acquisition physics requires expensive stochastic Monte Carlo sampling to approximate the point spread function (PSF). In this work, we propose a shift from neural network based implicit representations to Gaussian based explicit representations. By parameterizing the HR 3D image volume as a field of anisotropic Gaussian primitives, we leverage the property of Gaussians being closed under convolution and thus derive a \textit{closed-form analytical solution} for the forward model. This formulation reduces the previously intractable acquisition integral to an exact covariance addition ($\mathbf{\Sigma}_{obs} = \mathbf{\Sigma}_{HR} + \mathbf{\Sigma}_{PSF}$), effectively bypassing the need for compute-intensive stochastic sampling while ensuring exact gradient propagation. We demonstrate that our approach matches the reconstruction quality of self-supervised state-of-the-art SVR frameworks while delivering a 5$\times$--10$\times$ speed-up on neonatal and fetal data. With convergence often reached in under 30 seconds, our framework paves the way towards translation into clinical routine of real-time fetal 3D MRI. Code will be public at {this https URL}.
Abstract (translated)
从稀疏或退化的2D图像中恢复高保真度的3D图像是医学成像中的一个基本挑战，其应用范围广泛，涵盖了从3D超声重建到MRI超分辨率等各个领域。在胎儿MRI的情境下，从运动损坏的低分辨率2D采集数据中进行高分辨率3D脑部重建是准确诊断神经发育状况的前提条件。尽管基于隐式神经表示（INRs）的方法最近在自监督切片到体积重建（SVR）方面取得了最先进的性能，但它们面临一个关键的计算瓶颈：精确建模图像获取物理特性需要昂贵的随机蒙特卡洛采样来近似点扩散函数（PSF）。在这项工作中，我们提出了一种从基于神经网络的隐式表示转向基于高斯的显式表示的方法。通过将HR 3D图体积参数化为各向异性高斯基本单元的集合，我们可以利用高斯卷积闭合性质，并推导出前向模型的“封闭形式解析解”。这种表述将之前难以处理的获取积分简化为精确的协方差加法（$\mathbf{\Sigma}_{obs} = \mathbf{\Sigma}_{HR} + \mathbf{\Sigma}_{PSF}$），从而有效地绕过了计算密集型随机采样的需求，同时确保了准确的梯度传播。我们证明我们的方法在重建质量上与最先进的自监督SVR框架相匹配，并且在新生儿和胎儿数据集上的速度提高了5到10倍。通常情况下，在不到30秒的时间内就能达到收敛，这使得我们的框架朝着将实时胎儿3D MRI技术应用于临床实践迈进了一步。 代码将在[此处](https://this-url-will-be-provided)公开发布。
URL
https://arxiv.org/abs/2512.11624
