Volume 57, Number 11, 2003 APPLIED SPECTROSCOPY 1353 0003-7028 / 03 / 5711-1353$2.00 / 0 q 2003 Society for Applied Spectroscopy Band-Target Entropy Minimization (BTEM) Applied to Hyperspectral Raman Image Data EFFENDI WIDJAJA, NICOLE CRANE, TSO-CHING CHEN, MICHAEL D. MORRIS,* MICHAEL A. IGNELZI, JR., and BARBARA R. M CCREADIE Department of Chemistry (E.W., N.C.,T.-c.C., M.D.M.), Department of Pediatric Dentistry (M.A.I., Jr.), and Orthopaedics Research Laboratories (B.R.McC.), University of Michigan, Ann Arbor, Michigan 48109 Band-target entropy minimization (BTEM) has been applied to ex- traction of component spectra from hyperspectral Raman images. In this method singular value decomposition is used to calculate the eigenvectors of the spectroscopic image data set. Bands in non-noise eigenvectors that would normally be used for recovery of spectra are examined for localized spectral features. For a targeted (iden- tied) band, information entropy minimization or a closely related algorithm is used to recover the spectrum containing this feature from the non-noise eigenvectors, plus the next 5–30 eigenvectors, in which noise predominates. Tests for which eigenvectors to include are described. The method is demonstrated on one synthesized Ra- man image data set and two bone tissue specimens. By inclusion of small amounts of signal that would be unused in other methods, BTEM enables the extraction of a larger number of component spectra than are otherwise obtainable. An improvement in signal/ noise ratio of the recovered spectra is also obtained. Index Headings: Hyperspectral Raman imaging; Self-modeling curve resolution; SMCR; Band-target entropy minimization; BTEM; Fac- tor analysis. INTRODUCTION Self-modeling curve resolution (SMCR) is a major tool for extraction of information in vibrational spectroscopic imaging because an image data set may contain tens of thousands of mixture spectra. The goal is to extract chem- ical information and spatial distribution without any a priori information about the composition of the object being imaged. The problem is simplest in Raman spec- troscopy because a mixed component spectrum is just a linear superposition of the pure component spectra and these each scale with the number of scattering centers. Because the data set is over-determined, most workers have applied multivariate data reduction schemes to their image data. One problem is that there are an innite num- ber of linear combinations of the underlying spectra, so nding a unique and physically realistic solution requires constraints. Typical constraints include non-negativity, closure, and selectivity (peak shape, usually expressed as a maximum allowable width of a second derivative). 1 To date, none of the chemometrics tools that have been applied to the problem have been completely satisfactory. While most of them appear to work well on rather simple systems containing chemical components in similar pro- portions, they may fail to resolve minor components in complex systems or in systems in which relative amounts vary widely. The rst multivariate SMCR method to analyze vibra- Received 6 May 2003; accepted 7 July 2003. * Author to whom correspondence should be sent. tional spectroscopic image data was developed by Drumm and Morris. 2 They utilized interactive manual ei- genvector rotation following principal component analy- sis (PCA) to transform abstract chemical factors into meaningful pure component Raman spectra. Non-nega- tivities of pure spectra and associated scores and partic- ular band shapes were used as transformation constraints. This PCA-based method has been successfully applied to Raman imaging data obtained from a wide variety of syn- thetic materials and biological specimens. 2–11 The advan- tage of this approach is that it reduces the large data set into a small number of principal components, and the pure component spectra of observable components are well resolved even if there are low signal-to-noise ratios in the spectra at individual pixels. Other approaches have been applied. Multivariate curve resolution–alternating least squares (MCR-ALS) has been employed to analyze Raman image data of poly- styrene spheres in water and of emulsions of detergent components. 12 Hopke and co-workers have proposed a modied alternating least-squares procedure to reduce computational time required for curve resolution of sim- ilar image systems. 13 In addition to using the same MCR- ALS method, Fulghum and Artyushkova 14 have applied evolving factor analysis (EFA) and Simplisma to a sim- ilar problem: resolution of chemical components from X- ray photoelectron spectroscopy (XPS) images acquired from blends of poly(vinyl chloride) and poly(methyl methacrylate). Recently, Batonneau et al. applied Sim- plisma to analyze crystal powder spectra acquired using confocal Raman microspectrometry. 15 Recently, a newly developed SMCR method, band-tar- get entropy minimization (BTEM), has been applied to Fourier transform infrared (FT-IR) reaction data of or- ganometallic and homogeneous catalytic reactions 16–20 and FT-Raman data of environmental lead compounds. 21 It was shown that BTEM could recover minor compo- nents having very weak spectral signals. BTEM also en- hanced the signal-to-noise ratio of the recovered pure component spectra. BTEM is an example of a nonlinear constrained optimization approach, which uses important concepts from information-entropy theory. 22 In this paper we investigate the use of BTEM in the Raman imaging case and demonstrate its ability to resolve or extract com- ponents that are missed by older methods. In the information theory context, entropy, H , is a mea- sure of the disorder of a system or the degree of infor- mation dispersion across the data set, and is dened by Eq. 1: