AI 中文总结
该研究将Vaisman几何与Neifeld分析方法结合，提出新的几何分解框架，解决欠定逆问题歧义，实现抗噪、可处理的图像识别相关重建，可应用于多科学领域。
AI 中文摘要
我们提出一种从不完整数据中重建隐藏结构的新方法，在Vaisman和Neifeld的框架内统一几何积分与拓扑分析技术。该方法对构形空间进行精细几何分解，得到不变叶状结构与矩映射，从而解决欠定逆问题的内在歧义。结合Vaisman的对称性见解与Neifeld的分析方法，我们建立了鲁棒、抗噪的框架，确保计算可处理性，同时为成像与结构分析中的重建提供统一视角。此方法可应用于多个科学领域，凸显几何与拓扑在逆问题求解中的相互作用。
英文摘要
We introduce a new approach to the reconstruction of hidden structures from incomplete data, unifying techniques from geometric integration and topological analysis within the frameworks of Vaisman and Neifeld. Our method employs a refined geometric decomposition of configuration spaces into invariant foliations and moment maps, thereby addressing the intrinsic ambiguities of underdetermined inverse problems. By combining Vaisman's insights into symmetry with Neifeld's analytical methodologies, we establish a robust, noise-resistant framework that ensures computational tractability while providing a unified perspective on reconstruction in imaging and structural analysis. This approach enables applications across diverse scientific domains and highlights the interplay between geometry and topology in the solution of inverse problems.
DOI：10.1007/978-3-032-03918-7_24
