A regularized nonnegative canonical polyadic decomposition algorithm with preprocessing for 3D fluorescence spectroscopy

Abstract

International audienceWe consider blind source separation in chemical analysis focussing on the 3D fluorescence spectroscopy framework. We present an alternative method to process the Fluorescence Excitation-Emission Matrices (FEEM): first, a preprocessing is applied to eliminate the Raman and Rayleigh scattering peaks that clutter the FEEM. To improve its robustness versus possible improper settings, we suggest to associate the classical Zepp's method with a morphological image filtering technique. Then, in a second stage, the Canonical Polyadic (CP or Cande-comp/Parafac) decomposition of a nonnegative 3-way array has to be computed. In the fluorescence spectroscopy context, the constituent vectors of the loading matrices should be nonnegative (since standing for spectra and concentrations). Thus, we suggest a new NonNegative third order CP decomposition algorithm (NNCP) based on a non linear conjugate gradient optimisation algorithm with regularization terms and periodic restarts. Computer simulations performed on real experimental data are provided to enlighten the effectiveness and robustness of the whole processing chain and to validate the approach

Tensor-decomposed vibrational coupled-cluster theory: Enabling large-scale, highly accurate vibrational-structure calculations

“…The timings are normalized with respect to the time of the calculation using the dynamic scheme of Eq. (37). The results show that the dynamic scheme outperforms the two others with respect to speed regardless of the choice of ∆R in .…”

“…The CP format (also known in the literature as CAN-DECOMP/PARAFAC 30 ) has been applied in many contexts, e.g., analysis of 3-dimensional flourescence spectra, 36,37 and 0021-9606/2018/148(2)/024103/18/$30.00…”

A new penalized nonnegative third‐order tensor decomposition using a block coordinate proximal gradient approach: Application to 3D fluorescence spectroscopy

“…Therefore, in the context of the 3D fluorescence spectroscopy analysis (assuming the absence of errors coming either from the preprocessing used to remove Raman and Rayleigh scattering or possible bad settings of the devices), nonnegativity constraints should be considered given the physical nature of the hidden variables. In fact, in this particular application (see the work of Royer et al for a reminder of the links that exist between 3D fluorescence spectroscopy and CPD), the loading vectors stand for physical quantities intrinsically nonnegative since they are related to emission and excitation spectra and concentrations through the samples acquired at different times in monitoring applications (or locations or pH for other kinds of applications). The rank of the canonical polyadic model that will approximate the “observed” tensor is closely linked to the number of fluorescent chemical compounds that are present in the studied samples.…”

“…The nonnegativity of both the considered datasets and the quantities that have to be estimated is also crucial for numerous other leading applications of CPD, especially those encountered in the area of image processing (for example, hyperspectral imaging, computer vision, biomedical image processing, or functional magnetic resonance imaging for brain mapping). It is the reason why it has given rise to numerous nonnegative CPD algorithms (see the work of Cichocki et al or Royer et al for example for an overview of those nonnegative tensor factorization [NTF] algorithms).…”

A New Stochastic Optimization Algorithm to Decompose Large Nonnegative Tensors

“…Moreover, in a number of leading application areas of tensors (like fluorescence spectroscopy [10] [11] or image processing (remote sensing and hyperspectral imaging [12]) for example) the data sought (i.e. the constituent vectors of the loading matrices involved in the CP decomposition) should be nonnegative since they stand for intrinsically nonnegative physical quantities (for example emission and excitation spectra and concentrations in 3D fluorescence).…”