Composing hybrid wavelets for optimum and near‐optimum representation and accelerated evaluation of N‐way data sets

In hyphenated measurement devices, temporal, spatial, and spectral resolutions continue to increase. While this is advantageous from a chemical sensing perspective, the amount of data grows exponentially; this imposes challenges on Chemometric algorithms resulting in long computation times. In online sensing, however, time resolution is of vital importance and time delays introduced by lengthy computations become unacceptable. Further, in many applications, data need to be documented and a continuous stream of large data sets presents another technical burden regarding archiving space. This work builds on the previous wavelet studies that have already been published. It was found that there is no reason to use the same wavelet for all dimensions of a data set. ‘Hybrid wavelets’ were introduced which combine different wavelets; this facilitates fine-tuning of the compression. The challenge in using hybrid wavelets lies in the very large number of possible wavelet combinations. A method is presented that automatically determines the optimum and near-optimum wavelet combinations for a given data set. These wavelet combinations are found by evaluating each dimension of the data set separately. This procedure enables an optimization of computation speed, compressed data set size and accuracy of the Chemometric model. Two data cubes acquired from two different experiments are used to show the selection algorithm's capabilities. These examples demonstrate that this algorithm selects hybrid wavelets that are superior to randomly selected wavelet combinations regarding data approximation, compressed data set size, and acceleration of computations. Copyright © 2007 John Wiley & Sons, Ltd.