Chemical identification under a poisson model for Raman spectroscopy

Raman spectroscopy provides a powerful means of chemical identification in a variety of fields, partly because of its non-contact nature and the speed at which measurements can be taken. The development of powerful, inexpensive lasers and sensitive charge-coupled device (CCD) detectors has led to widespread use of commercial and scientific Raman systems. However, relatively little work has been done developing physics-based probabilistic models for Raman measurement systems and crafting inference algorithms within the framework of statistical estimation and detection theory.;The objective of this thesis is to develop algorithms and performance bounds for the identification of chemicals from their Raman spectra. This involves the following thrusts:;• Measurement Model: A Poisson measurement model based on the physics of a dispersive Raman device is presented. Placing a statistical model on parameters and data allows one to draw on information theory to quantify how much information needed for the required task is available in the data provided by the sensor.;• Parameter Estimation: The problem is expressed as one of deterministic parameter estimation, and several methods are analyzed for computing the maximum-likelihood (ML) estimates of the mixing coefficients under our data model. The performance of these algorithms is compared against the Cramér-Rao lower bound (CRLB). The non-negative iteratively reweighted least squares (NNIRLS) algorithm is seen to give performance that is nearly identical to the more computationally demanding expectation-maximization approach.;• Target Detection: The Raman detection problem is formulated as one of multiple hypothesis detection (MHD), and an approximation to the optimal decision rule is presented. The resulting approximations are related to the minimum description length (MDL) approach to inference. In our simulations, this method is seen to outperform two common general detection approaches, the spectral unmixing approach and the generalized likelihood ratio test (GLRT). The MHD framework is applied naturally to both the detection of individual target chemicals and to the detection of chemicals from a given class.;• Accounting for Unknown Chemicals: The common, yet vexing, scenario is considered in which chemicals are present that are not in the known reference library. A novel variation of nonnegative matrix factorization (NMF) is developed to address this problem. Our simulations indicate that this algorithm gives better estimation performance than the standard two-stage NMF approach and the fully supervised approach when there are chemicals present that are not in the library.;• Dealing with Library Error: Estimation algorithms are developed that take into account errors that may be present in the reference library. In particular, an algorithm is presented for ML estimation under a Poisson errors-in-variables (EIV) model. It is shown that this same basic approach can also be applied to the nonnegative total least squares (NNTLS) problem.;Most of the techniques developed in this thesis are applicable to other problems in which an object is to be identified by comparing some measurement of it to a library of known constituent signatures.