AI 中文总结
TENSKEL是一种基于离散域张量表示的组合可观测框架，可明确测量诱导的潜构型组织，为结构化测量与重建提供数学基础，在多领域具有潜在应用
AI 中文摘要
许多成像问题旨在从部分可观测测量中重建底层构型。尽管重建算法基于这些测量运行，但测量过程诱导的可观测组织却很少被明确表示。我们引入TENSKEL，一种基于离散域上定义的张量表示、用于结构化测量与重建的组合可观测框架。从二元潜集合出发，该框架通过连续聚合与折叠操作，构建了将测量上下文耦合到潜Pascal组织的张量层级。每个测量上下文诱导出同一潜集合的可观测划分，所得张量形式明确了相关的组合多重性、壳层组织、简并度及诱导的重建几何。该框架未引入新的重建算法，而是提供了潜构型在观测下如何组织的数学表示。诱导的张量核通过潜坐标的测量上下文响应表征其相似性，而正则化反演则从可观测测量中提供潜表示的结构化重建。该二元构造还自然地扩展到离散单形支撑的潜表示的多项形式。与Pascal元胞自动机和结构化离散颜色映射的联系分别说明了该框架的压缩和多项实现。更广泛地说，TENSKEL为推理观测诱导的组织提供了组合基础，在计算成像、逆问题、结构化传感及量子启发的测量公式等领域具有潜在应用价值。
英文摘要
Many imaging problems seek to reconstruct underlying configurations from partial observable measurements. While reconstruction algorithms operate on these measurements, the observable organization induced by the measurement process is rarely represented explicitly. We introduce TENSKEL, a combinatorial observable framework for structured measurement and reconstruction based on tensor representations defined over discrete domains. Starting from a binary latent ensemble, the framework constructs a hierarchy of tensors coupling measurement contexts to a latent Pascal organization through successive aggregation and folding operations. Each measurement context induces an observable partition of the same latent ensemble, and the resulting tensor formulation makes explicit the associated combinatorial multiplicities, shell organization, degeneracies, and induced reconstruction geometry. Rather than introducing a new reconstruction algorithm, this framework provides a mathematical representation of how latent configurations become organized under observation. The induced tensor kernel characterizes similarities between latent coordinates through their measurement-context responses, while regularized inversion provides a structured reconstruction of the latent representation from observable measurements. The binary construction further admits a natural multinomial extension to discrete simplex-supported latent representations. Connections to Pascal cellular automata and structured discrete color mappings illustrate respectively compressed and multinomial realizations of the framework. More generally, TENSKEL provides a combinatorial basis for reasoning about the organization induced by observation, with potential relevance to computational imaging, inverse problems, structured sensing, and quantum-inspired measurement formulations.
Comments15 pages, 2 figures, 1 appendix. Accepted for presentation at the IEEE ICIP 2026 Workshop on Quantum Computing and Quantum-Inspired Methods for Imaging (QCI 2026); withdrawn from the proceedings because the author was unable to attend the conference
