ADT: Sparse Blind Separation Algorithms of Spectral Mixtures and Applications

化学和生物制剂的光谱传感既是国家安全的一个关键领域，也是一个充满活力的科学领域。虽然现代成像和光谱学技术已经使通过光谱对纯化学物质进行分类成为可能，但实际的现场数据往往包含化学物质的混合物，受到不断变化的背景和环境噪声的影响。在这个项目中，研究者和他的同事们开发了信号处理算法及其数学分析，用于噪声条件下光谱混合的盲分离。盲源分离（BSS）方法的目的是在不知道混合环境的情况下从混合信号中提取信息。一个主要的挑战是光谱数据是相关的，传统的“统计独立性”不能作为一个很好的分离标准。取而代之的是利用比独立性更弱的局部谱稀疏条件。备选准则导致一个可由凸规划解决的优化问题。压缩感知（CS）算法的最新进展也发挥了作用。由此产生的BSS-CS算法有望盲目分离比光谱测量数量更多的化学物质。BSS-CS算法还将作为一种预处理工具，用于初始化和改进非凸优化方法的收敛性，例如针对化学物质一般光谱条件的非负矩阵分解方法。化学物质往往太小，人眼无法识别。它们被传感设备根据它们的频率内容（光谱）捕获。虽然纯化学物质的光谱可以通过目测来识别，但化学混合物的光谱形式复杂多样，给分析带来了严峻的挑战。化学混合物在环境中很常见。该项目的目标是开发一套新的鲁棒分离算法，用于在现实条件下测量化学和生物混合物。一个关键问题是恢复化学混合物中单个成分的光谱，并分析其潜在危害和损害的程度。计算和有关技术对于查明在环境中释放的潜在危险化学品和为决策者及时采取行动提供有价值的资料将是必不可少的。研究者及其同事应采用新的数学技术和信号处理方法来提高基于光谱数据的化学传感和识别的计算能力。

Spectral sensing of chemical and biological agents is both a critical area of national security and a vibrant scientific area. Though modern imaging and spectroscopy technology have made it possible to classify pure chemicals by spectra, realistic field data often contain mixtures of chemicals, subject to changing background and environmental noise. In this project, the investigator and his colleagues develop signal processing algorithms and their mathematical analysis for blind separation of spectral mixtures in noisy conditions.Blind source separation (BSS) methods aim to extract the information of source signals from their mixtures without knowledge of the mixing environment.A major challenge is that the spectral data are correlated and the conventional ``statistical independence'' fails to be a good separation criterion. Instead, a local spectral sparseness condition weaker than independence will be utilized. The alternative criterion leads to an optimization problem solvable by convex programming. Recent advances in compressive sensing (CS) algorithms are also brought into play. The resulting BSS-CS algorithms are promising for blindly separating more chemicals than the number of spectral measurements. The BSS-CS algorithm will also serve as a preprocessing tool to initialize and improve the convergence of nonconvex optimization methods such as the nonnegative matrix factorization methods for general spectral conditions of chemicals.Chemicals are often too small to be identified by human eyes. They are captured by sensing equipment in terms of their frequency contents (spectra). Though spectra of pure chemicals can be identified by visual inspection, the spectra of chemical mixtures take a variety of complicated forms and pose a serious challenge for analysis. Chemical mixtures are quite common in the environment. The goal of the project is to develop a new suite of robust separation algorithms for chemical and biological mixtures measured in realistic conditions. A critical issue is to recover the spectra of the individual components of chemical mixtures, and analyze the level of their potential harm and damage. The computation and related technology will be essential for identifying potentially dangerous chemicals released in the environment and for providing valuable information for decision makers to act timely. The investigator and his colleagues shall employ new mathematical techniques and signal processing methods to enhance the computational capability of chemical sensing and identification based on spectral data.