Correcting inner filter effects, a non multilinear tensor decomposition method

• A non multilinear approach to include inner filter effects in fluorescence spectroscopy
• A theoretical framework on identifiability of non multilinear tensor models
• An algorithm to recover the factors in the decomposition
• Results obtained with real data

Among measurement used in analytical chemistry, fluorescence spectroscopy is widely spread and its applications are numerous. To recover various information on unknown components in chemical mixtures, multilinear tensor decomposition of multiway fluorescence spectra has proven extremely powerful. However, inner filter effects induce a systematic error on measurements, disturbing the decomposition. In this paper, we fully describe a non multilinear approach to include inner filter effects in the model instead of neglecting them or correcting them by linearization methods. A theoretical framework on non multilinear tensor decomposition is developed, an algorithm to recover the factors in the decomposition is detailed, and real data computer results are reported.