This paper investigates a 2D to 3D image translation method with a
straightforward technique, enabling correlated 2D X-ray to 3D CT-like
reconstruction. We observe that existing approaches, which integrate
information across multiple 2D views in the latent space, lose valuable signal
information during latent encoding. Instead, we simply repeat and concatenate
the 2D views into higher-channel 3D volumes and approach the 3D reconstruction
challenge as a straightforward 3D to 3D generative modeling problem,
sidestepping several complex modeling issues. This method enables the
reconstructed 3D volume to retain valuable information from the 2D inputs,
which are passed between channel states in a Swin UNETR backbone. Our approach
applies neural optimal transport, which is fast and stable to train,
effectively integrating signal information across multiple views without the
requirement for precise alignment; it produces non-collapsed reconstructions
that are highly faithful to the 2D views, even after limited training. We
demonstrate correlated results, both qualitatively and quantitatively, having
trained our model on a single dataset and evaluated its generalization ability
across six datasets, including out-of-distribution samples.

该研究探讨了一种简单直接的二维到三维图像转换方法，通过重复和连接二维视图生成高通道的三维模型，解决了现有方法在潜在空间中整合信息时丢失信号信息的问题，并通过神经最优传输实现了在多个视角上无需精确对齐即可整合信号信息，训练结果在多个数据集上得出了定性和定量一致的重建效果。

重复与连接：2D 到 3D 图像转换通过 3D 到 3D 生成建模

Repeat and Concatenate: 2D to 3D Image Translation with 3D to 3D  Generative Modeling

We present a new extension for Neural Optimal Transport (NOT) training
procedure, capable of accurately and efficiently estimating optimal
transportation plan via specific regularisation on conjugate potentials. The
main bottleneck of existing NOT solvers is associated with the procedure of
finding a near-exact approximation of the conjugate operator (i.e., the
c-transform), which is done either by optimizing over maximin objectives or by
the computationally-intensive fine-tuning of the initial approximated
prediction. We resolve both issues by proposing a new, theoretically justified
loss in the form of expectile regularization that enforces binding conditions
on the learning dual potentials. Such a regularization provides the upper bound
estimation over the distribution of possible conjugate potentials and makes the
learning stable, eliminating the need for additional extensive finetuning. We
formally justify the efficiency of our method, called Expectile-Regularised
Neural Optimal Transport (ENOT). ENOT outperforms previous state-of-the-art
approaches on the Wasserstein-2 benchmark tasks by a large margin (up to a
3-fold improvement in quality and up to a 10-fold improvement in runtime).

通过对共轭势进行特定正则化，我们提出了一种用于神经最优输运（NOT）训练过程的新扩展，能够准确高效地估计最优传输方案。我们通过引入期望损失函数的正则化来解决现有 NOT 求解器的主要瓶颈问题，从而实现对学习双重潜力的限制条件，提供共轭势可能分布的上界估计，使学习过程稳定，消除了额外的广泛微调的需求。我们称之为期望损失正则化神经最优输运（ENOT）的方法在 Wasserstein-2 基准任务上明显优于先前的最新技术方法（质量提高 3 倍，运行时间提高 10 倍）。

ENOT: 快速准确的神经最优输运训练的 Expectile 正则化

ENOT: Expectile Regularization for Fast and Accurate Training of Neural  Optimal Transport

Neural optimal transport techniques mostly use Euclidean cost functions, such
as $\ell^1$ or $\ell^2$. These costs are suitable for translation tasks between
related domains, but they are hardly applicable to problems where a specific
non-Euclidean optimality of the mapping is required such as dataset transfer.
To tackle this issue, we introduce a novel neural network-based algorithm to
compute optimal transport plans and maps for general cost functionals. Such
functionals provide more flexibility and allow using auxiliary information,
such as class labels, to construct the required transport map. Our method is
based on a saddle point reformulation of the optimal transport problem and
generalizes prior methods for weak and strong transport cost functionals. As an
application, we construct a functional to map data distributions with
preserving the class-wise structure of data.

本文介绍了一种基于神经网络的新算法，用于计算一般的成本功能的最优输运方案和映射，该算法通过鞍点重构最优输运问题并推广到先前在弱和强输运成本功能中的方法，最终构建了一个可保存数据类别结构的数据分布映射功能。