Spectral sensing involves a range of technologies for detecting, identifying chemicals and biological agents. An important application is in homeland security where a critical problem is identification of unknown explosives. Though the advances of modern spectroscopy technology have made it possible to classify pure chemicals by spectra, realistic data are often composed of mixtures of chemicals and environmental noise.

In most cases, one has to deal with a so called blind signal(source) separation (BSS) problem. Conventional approaches such as NMF and ICA are non-convex and too general to be robust and reliable in real-world applications. Based on a partial knowlege of the data (e.g. local spectral sparseness), we are able to reduce the problem to a series of convex sub-problems. Compressive sensing algorithms are also brought into play. The methods will be illustrated in processing of datasets from NMR, DOAS,and Raman spectroscopy.