ADT: Sparse Blind Separation Algorithms of Spectral Mixtures and Applications

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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.