A hierarchical local weighted calibration and classification approach to depth-resolved quantification in scattering media using photon time-of-flight measurements

Chemometric methods for quantitative analysis in layered scattering/absorbing paper samples are described. A radial array of time-resolved diffuse reflectance measurements have been made to obtain multi-perspective information sensitive to changing sample composition. For analysis, the stepwise multilinear regression (SMLR) method was used a basis of a hierarchical locally weighted sample calibration. Estimates of the absorption coefficient in each sample region were made either by linear regression following by binning of the result (HLRB) or by K-nearest neighbour classification analysis (HCKNN). With these approaches, the tomographic reconstruction problem may be linearized by utilizing a priori information about sample composition in upper regions to direct subsequent calibrations for lower regions. A comparison of different reconstruction methodologies is made along with their efficacy in the presence of added noise. Results demonstrate that estimations of the absorption coefficient deep within a highly scattering/absorbing sample are obtainable at greater than 50% accuracy, using the HCKNN approach. This represents a 20% improvement at all sample depths over the SMLR approach. The use of locally weighted calibrations and sample classification to constrain the solution of a tomographic reconstruction is shown as a powerful new tool for quantification in layered scattering/absorbing media.