CCSS: Block-term Tensor Tools for Multi-aspect Sensing and Analysis

CCSS：用于多方面传感和分析的块项张量工具

• 批准号: 2024058
• 负责人: Xiao Fu
• 金额: $ 36万
• 依托单位: Oregon State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2020
• 资助国家: 美国
• 起止时间: 2020-09-15 至 2024-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2024058&HistoricalAwards=false
• 关键词: CCSS; Block; term; Tensor; Tools

Multi-aspect data arise ubiquitously in sensing, communications, and signal processing. For example, a hyperspectral image in remote sensing has two spatial aspects and one spectral aspect; spectrum dynamics data in wireless communications comprise frequency, time, and space aspects. As higher-order extensions of matrices, tensor models are considered indispensable tools for multi-aspect sensing and analytics. This project is concerned with a recently emerged tensor decomposition model, namely, the block-term decomposition model in multilinear rank-(L,L,1) terms (i.e., the LL1 model). This model is well-aligned to the underlying physics of a number of core applications in remote sensing, medical imaging, chemometrics, and wireless communications, thereby offering strong theoretical guarantees for these tasks. However, the LL1 model is relatively new, and thus many challenges pertaining to its theory and methods (e.g., scalability, robustness, and missing value recoverability) are still largely uncharted territories. The appealing promises for boosting performance of engineering applications have been barely fleshed out. This project will significantly advance the understanding to the computational and analytical aspects of the LL1 model --- leading to a series of theory-backed refreshing multi-aspect data acquisition and processing algorithms. Beyond engineering, the developed theory and methods will also be broadly applicable in related domains such as ecology, biology and food science, where multi-aspect data frequently come up. The project will also offer opportunities for training undergraduate students in optimization, linear algebra, and real-data acquisition.Towards fully capitalizing the power of the LL1 tensor model, this project will address a number of critical challenges in LL1 decomposition theory and methods. Specifically, the first thrust will design scalable LL1 algorithms that can flexibly incorporate a large variety of prior information as constraints and regularization; the second thrust will develop model identification guarantees and algorithms for LL1 computations in the presence of gross outliers; the third thrust will develop theory and algorithms for recovering compressed/downsampled LL1 tensors; and the last thrust applies the proposed approaches onto real-world engineering problems such as hyperspectral unmixing, fluorescence data analysis, hyperspectral super-resolution, and spectrum cartography. The proposed computational and analytical tools are well-motivated in wake of the rapid growth of multi-aspect data. Optimization problems associated with LL1 tensor decomposition are hard in both theory and practice, due to their nonconvex nonsmooth nature and the LL1 model’s inherent ill-conditioned multilinear structure. Outlier-robust LL1 decomposition and compressed/downsampled LL1 tensor recovery pose exciting research questions that reside at the core of signal processing and data analytics. The solutions developed in this project will offer new insights and effective tools for these challenging open problems, which are bound to benefit a broad range of real-world applications.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

多方面数据在传感、通信和信号处理中无处不在。例如，遥感中的高光谱图像具有两个空间方面和一个光谱方面;无线通信中的频谱动态数据包括频率、时间和空间方面。作为矩阵的高阶扩展，张量模型被认为是多方面传感和分析不可或缺的工具。本课题研究的是最近出现的一种张量分解模型，即多线性秩-（L，L，1）项的块项分解模型（即，LL 1模型）。该模型与遥感、医学成像、化学计量学和无线通信等核心应用的基础物理非常吻合，从而为这些任务提供了强有力的理论保证。然而，LL 1模型相对较新，因此与其理论和方法有关的许多挑战（例如，可伸缩性、健壮性和缺失值可恢复性）仍然是很大程度上未知的领域。提高工程应用性能的诱人承诺几乎没有得到充实。该项目将显著推进对LL 1模型的计算和分析方面的理解-导致一系列理论支持的刷新多方面数据采集和处理算法。除了工程之外，开发的理论和方法也将广泛适用于相关领域，如生态学，生物学和食品科学，其中经常出现多方面的数据。该项目还将为本科生提供优化、线性代数和真实数据采集方面的培训机会。为了充分利用LL 1张量模型的能力，该项目将解决LL 1分解理论和方法中的一些关键挑战。具体来说，第一个推力将设计可扩展的LL 1算法，可以灵活地将大量的先验信息作为约束和正则化;第二个推力将开发模型识别保证和算法，用于在存在总异常值的情况下计算LL 1;第三个推力将开发理论和算法，用于恢复压缩/下采样的LL 1张量;最后一个重点是将所提出的方法应用于现实世界的工程问题，如高光谱解混、荧光数据分析、高光谱超分辨率和光谱制图。所提出的计算和分析工具在多方面数据的快速增长之后得到了很好的激励。与LL 1张量分解相关的优化问题在理论和实践中都很困难，这是由于它们的非凸非光滑性质和LL 1模型固有的病态多线性结构。异常鲁棒LL 1分解和压缩/下采样LL 1张量恢复提出了令人兴奋的研究问题，这些问题位于信号处理和数据分析的核心。该项目开发的解决方案将为这些具有挑战性的开放问题提供新的见解和有效的工具，这必将使广泛的现实应用受益。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

项目成果

Fast and Structured Block-Term Tensor Decomposition for Hyperspectral Unmixing

• DOI: 10.1109/jstars.2023.3238653
• 发表时间: 2022-05
• 期刊: IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing
• 影响因子: 5.5
• 作者: Meng Ding;Xiao Fu;Xile Zhao

Deep Spectrum Cartography: Completing Radio Map Tensors Using Learned Neural Models

• DOI: 10.1109/tsp.2022.3145190
• 发表时间: 2021-05
• 期刊: IEEE Transactions on Signal Processing
• 影响因子: 5.4
• 作者: S. Shrestha;Xiao Fu;Min-Fong Hong

Hyperspectral Super-Resolution via Interpretable Block-Term Tensor Modeling

通过可解释的块项张量建模实现高光谱超分辨率

• DOI: 10.1109/jstsp.2020.3045965
• 发表时间: 2020-06
• 期刊: IEEE Journal of Selected Topics in Signal Processing
• 影响因子: 7.5
• 作者: Meng Ding;Xiao Fu;Ting-Zhu Huang;Jun Wang;Xi-Le Zhao
• 通讯作者: Xi-Le Zhao

Deep Generative Model Learning For Blind Spectrum Cartography with NMF-Based Radio Map Disaggregation

• DOI: 10.1109/icassp39728.2021.9413382
• 发表时间: 2021-06
• 期刊: ICASSP 2021 - 2021 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)
• 作者: S. Shrestha;Xiao Fu;Min-Fong Hong

Constrained Block-Term Tensor Decomposition-Based Hyperspectral Unmixing via Alternating Gradient Projection

通过交替梯度投影基于约束块项张量分解的高光谱分解

• DOI: 10.23919/eusipco54536.2021.9616213
• 发表时间: 2021
• 期刊: EUSIPCO 2021
• 作者: Ding, Meng;Fu, Xiao;Huang, Ting-Zhu;Zhao, Xi-Le
• 通讯作者: Zhao, Xi-Le