Multi-exponential Lifetime Extraction in Time-Logarithmic Scale

Methods are proposed for estimating real lifetimes and corresponding coefficients from realvalued measurement data in logarithmic scale, where the data are multi-exponential, i.e. represented by linear combinations of decaying exponential functions with various lifetimes. Initial approximations of lifetimes are obtained as peaks of the first derivative of the data, where the first derivative can, e.g, be calculated in the spectral domain using the cosine Fourier transform. The coefficients corresponding to lifetimes are then estimated using the linear least squares fitting. Finally, all the coefficients and the lifetimes are optimized using the values previously obtained as initial approximations in the non-linear least squares fitting. We can fit both the data curve and its first derivative and allow simultaneous analysis of multiple curves. Industrial Conference on Data Mining (ICDM) This work may not be copied or reproduced in whole or in part for any commercial purpose. Permission to copy in whole or in part without payment of fee is granted for nonprofit educational and research purposes provided that all such whole or partial copies include the following: a notice that such copying is by permission of Mitsubishi Electric Research Laboratories, Inc.; an acknowledgment of the authors and individual contributions to the work; and all applicable portions of the copyright notice. Copying, reproduction, or republishing for any other purpose shall require a license with payment of fee to Mitsubishi Electric Research Laboratories, Inc. All rights reserved. Copyright c © Mitsubishi Electric Research Laboratories, Inc., 2016 201 Broadway, Cambridge, Massachusetts 02139 Multi-exponential Lifetime Extraction in Time-logarithmic Scale Andrew V. Knyazev, Qun Gao, and Koon Hoo Teo Mitsubishi Electric Research Labs (MERL) 201 Broadway, Cambridge, MA 02139, USA Abstract. Methods are proposed for estimating real lifetimes and corresponding coefficients from real-valued measurement data in logarithmic scale, where the data are multi-exponential, i.e. represented by linear combinations of decaying exponential functions with various lifetimes. Initial approximations of lifetimes are obtained as peaks of the first derivative of the data, where the first derivative can, e.g, be calculated in the spectral domain using the cosine Fourier transform. The coefficients corresponding to lifetimes are then estimated using the linear least squares fitting. Finally, all the coefficients and the lifetimes are optimized using the values previously obtained as initial approximations in the non-linear least squares fitting. We can fit both the data curve and its first derivative and allow simultaneous analysis of multiple curves. Methods are proposed for estimating real lifetimes and corresponding coefficients from real-valued measurement data in logarithmic scale, where the data are multi-exponential, i.e. represented by linear combinations of decaying exponential functions with various lifetimes. Initial approximations of lifetimes are obtained as peaks of the first derivative of the data, where the first derivative can, e.g, be calculated in the spectral domain using the cosine Fourier transform. The coefficients corresponding to lifetimes are then estimated using the linear least squares fitting. Finally, all the coefficients and the lifetimes are optimized using the values previously obtained as initial approximations in the non-linear least squares fitting. We can fit both the data curve and its first derivative and allow simultaneous analysis of multiple curves.