Introducing multi‐dimensional ‘hybrid wavelets’ for enhanced evaluation of hyperspectral image cubes and multi‐way data sets

Abstract

AbstractMulti‐dimensional wavelet transforms (WTs) have been introduced for efficient data compression in order to accelerate chemometric calculations and to reduce requirements for data storage space. For hyphenated measurement techniques or hyperspectral imaging this wavelet compression becomes vital because such sensors acquire unprecedented amounts of information in short periods of time. Conventional, multi‐dimensional wavelet compression uses the same wavelet for all dimensions. However, from a mathematical perspective there is no need for this restriction as the transforms in different dimensions are independent from each other. This manuscript presents multidimensional ‘hybrid wavelet transforms’, which utilize different wavelet types for different dimensions. Thus, hybrid wavelets optimize wavelet compression by adjusting WTs to the different types of data sets. In this manuscript we demonstrate that hybrid wavelets improve acceleration factors compared to conventional multi‐dimensional wavelet compression and determine more precise models. Combinations of Haar, Daub4, Daub6, Daub8, Daub10, Daub12, Daub14, Daub16, Daub18 and Daub20 wavelets are considered in this study. Data obtained with two different experimental techniques are used for assessing hybrid wavelet compression: (i) a data cube obtained by means of mid‐infrared hyperspectral imaging; (ii) data acquired by excitation‐emission matrix (EEM) fluorescence spectroscopy in photo‐catalytic studies. For the hyperspectral data cube hybrid wavelets were found, which are superior regarding acceleration and model quality to all 10 conventional WTs (Haar–Daub20). For the EEM example this was achieved in 9 out of 10 cases; thus in 19 out of 20 investigated cases hybrid WTs were found to be superior to conventional wavelet compression. Copyright © 2006 John Wiley & Sons, Ltd.