ATD: Blind and Template Assisted Source Separation Algorithms with Applications to Spectroscopic Data

光谱传感技术是检测和识别化学和生物物质的强大分析工具，因此广泛用于确定分子结构、爆炸物的远距离检测、空气成分成像等。然而，在现实世界中被成像的对象通常是混合物而不是纯物质，使得难以从现有的查找表或模板直接识别和量化化学成分。一个基本的科学问题是将测量的光谱数据解混或分解为基本成分（纯光谱或源光谱）的非冗余和紧凑组合，以便于随后基于查找表的验证和量化。主要研究员（PI）和他的团队根据源信号的可用知识（源信号模板的最小，部分或全部知识）研究三类解混问题。研究的问题是盲源、部分盲源和模板辅助源分离与识别。所提出的项目的智力价值是一个相结合的几何和统计方法与相关的计算算法，将稀疏正则化优化技术。几何方法是基于源信号的频谱的稀疏性，而统计方法是在源频谱的部分和统计知识可用时分解基于模板的数据拟合的误差。实验结果表明，所提出的方法适用于核磁共振、拉曼光谱和差分吸收光谱的实验室数据，PI及其团队对光谱混合物解混的数据分析和计算算法可以大大提高公共卫生和安全的威胁降低和决策能力。他们拟议的工作领域有能力对信息技术、生物技术、民用基础设施和环境安全产生广泛影响;特别是对战场上产生的化合物混合物的结构了解和威胁评估、国土安全、空气质量监测、代谢指纹和疾病诊断。在他们的项目中产生的数学工具和数值数据也有利于研究人员和研究生在数据共享和管理，课程开发和课程设置。PI积极参与指导博士后研究员的研究和职业发展。

Spectroscopic sensing techniques are powerful analytical tools for detecting and identifying chemical and biological substances, and so are widely used in determining molecular structures, stand-off detection of explosives, imaging of air composition to name a few. However, the objects being imaged in the real-world are more often mixtures than pure substances, making difficult direct identification and quantification of chemical constituents from existing lookup tables or templates. A fundamental scientific problem is to unmix or decompose the measured spectral data into a non-redundant and compact combination of basic components (pure or source spectra) facilitating subsequent verification and quantification based on look-up tables. The principal investigator (PI) and his team study three classes of unmixing problems depending on the available knowledge of the source signals (minimal, partial or full knowledge of a template of source signals). The research problems are blind, partially blind and template assisted source separation and identification. The intellectual merit of the proposed project is a combined geometrical and statistical approach with associated computational algorithms incorporating sparsity regularized optimization techniques. The geometric approach is based on the sparseness of the spectra of the source signals while the statistical approach is on decomposing the errors of template based data fitting when partial and statistical knowledge of the source spectra is available. The proposed methods are shown to be applicable to laboratory data from nuclear magnetic rensonance, Raman spectroscopy and differential optical absorption spectroscopy.The data analysis and computational algorithms on unmixing spectroscopic mixtures by the PI and his team can greatly improve the capability of threat reduction and decision making for public health and security. Their proposed line of work is well-positioned to generate broad impact on information technology, biotechnology, safety of civil infrastruture and environment; in particular the structural understanding and threat assessment of mixtures of chemical compounds originating in battle fields, homeland security, air quality monitoring, metabolic fingerprinting and disease diagnosis. The mathematical tools and numerical data produced in their project also benefit researchers and graduate students in data sharing and management, curriculum development and course offerings. The PI actively engages in mentoring postdoctoal fellows in terms of research and career advancement.