Recovery of Variable Loadings and Eigenvalues Directly from Fourier Compressed Ion Mobility Spectra

A discrete sine transform (DST) method has been devised for the Fourier compression of ion mobility spectra. The DST allows the calculation of eigenvalues with correct scale directly from the compressed data. A novel procedure for transforming the variable loadings from Fourier to native domains has been devised. For the first time, data may be interpreted in their native domain without decompression of the entire data set. This achievement is significant because results generated from the analysis of compressed data had been restricted to an abstract mathematical form. Methodology to convert these abstract results to a form that is understandable by analytical chemists is presented. This capability has important applications to the analysis of large data sets and embedded data processing under the constraints of miniaturized instrumentation. Five sets of evaluation data were obtained from vapor samples of formamide, 1-pentanol, and a mixture of two chemical warfare simulants (DIMP and DMMP) with a handheld ion mobility spectrometer (IMS). These data sets were compressed by 90% or more and reconstructed with 1% or less relative error. IMS instruments can generate thousands of spectra per hour. MATLAB functions for the DST, the inverse DST, and the two-dimensional DST are furnished in the Appendix.