Chemical Identification using Bayesian Model Selection

Remote detection and identification of chemicals in a scene is a challenging problem. We introduce an approach that uses some of the image’s pixels to establish the background characteristics while other pixels represent the target for which we seek to identify all chemical species present. This leads to a generalized least squares problem in which we focus on “subset selection” to identify the chemicals thought to be present. Bayesian model selection allows us to approximate the posterior probability that each chemical in the library is present by adding the posterior probabilities of all the subsets which include the chemical. We present results using realistic simulated data for the case with 1 to 5 chemicals present in each target and compare performance to a hybrid of forward and backward stepwise selection procedure using the F statistic. Introduction We consider infrared hyperspectral image data in which we first locate chemical plumes and then characterize the chemical components of the plume (McVey et. al., 2002). Our focus is chemical identification from a library of tens to hundreds of chemicals using a passive infrared (IR) detector several kilometers above the ground. A typical scene is 1000 x 128 pixels, where the detected signal at each pixel depends on the ground radiance, atmospheric transmission, instrument noise, and whether a chemical plume lies between the ground and the detector. A prior analysis identifies the plume pixels (pixels that have a plume influencing the signal) from among the background pixels (pixels that do not have a plume influencing the signal). Simplifying assumptions lead to a general least squares (GLS) problem for which we choose which subset (up to 3 chemicals from approximately 100 chemicals for example) of chemicals is most likely to be present in the plume. The next section presents a physical model and the assumptions to convert this to a GLS problem. Following sections present model selection approaches including Bayesian model averaging (BMA) and “pick the winner” (PW) using penalized likelihood (the F test is a special case). We present results with simulated data, and include cases where the errors do not have a Gaussian distribution and the predictors have nonnegligible measurement error. We conclude that the false positive and negative rates for BMA are similar to those for PW provided the appropriate penalty is used with PW. Background A hyperspectral detector detects photons emitted in the IR region from the ground. The signal from background pixel i is ( ) ( ) ( ) ( ) g b i i j j j i j i S L N ε ν ν τ ν ν = + (1), where ( ) i j ε ν is the emissivity at wavelength (or frequency) j ν , ( ) g j i L ν is the Planck function at ground temperature, ( ) j τ ν is the atmospheric transmission, and ( ) i j N ν is the noise. The signal from plume pixel i is ( )[ ( ) ( ) ( )] ( ) (2), p p g b p j j i j j j i i i i S L L S α ν ν ε ν ν τ ν = − + where ( ) p j α ν is the plume absorption and ( ) p j i L ν is the Planck function at plume temperature. The plume has two effects: it emits in the IR region, but it also absorbs the radiation emitted from itself and from the ground. The ( ) i j ε ν terms (emissitivites) depend on the properties of the background. Concrete, asphalt, buildings, grass, dirt, water, and other common background features each have their characteristic emissitivity. Our synthetic background scenes are generated from various mixtures of approximately 100 typical background emissitivites. Our synthetic plumes are generated from a library of approximately 100 chemical species of interest. Typically there are 10,000 to 16,000 pixels in a scene with 1 to a few plumes. The number of pixels in a plume is 10’s to 100’s. Spring Research Conference Section on Physical & Engineering Sciences (SPES)