Non-negative matrix factorization algorithm with sparcity constraints an application to in vivo spectrally resolved acquisitions
Résumé
Fluorescence imaging in diffusive media is an emerging diagnosis modality which locates specific targets (e.g tumors) thanks to injected fluorescent markers. The region of interest is illuminated with near infrared light and the emitted back fluorescence is analyzed to locate the fluorescence sources. Since the fluorescence signal decreases with the light travel distance, while the autofluorescence of biological tissues signal remains constant, autofluorescence removal is necessary to explore thick media. We propose a spectroscopic approach, based on a new Non-negative Matrix Factorization (NMF) algorithm with sparsity constraints, to unmix several fluorescence sources, including autofluorescence. An experiment is performed on a mouse to test our method: two capillary tubes respectively filled with 5 µl of Indocyanine Green loaded into nanoparticules (ICG-LNP) at 0.35 µM and 5µl of Alexa 750 at 0.1 µM are inserted subcutaneous to simulate marked targets. The animal is illuminated at 690 nm with a laser and the emitted back fluorescence signal is collected by an imaging spectrometer coupled with a CCD camera (Andor Technologies): a scanning of the animal is obtained (Figure 1, left). The spectrally resolved acquisition is processed with our NMF algorithm, which approximates data as the product of two non-negative matrices, one carrying the spectra information and the other the weighting factors of the fluorescence sources. A sparse constraint is imposed on specific markers weight factors, expected sparse enough to represent a local fluorescence signal. Link can be made between size of tumor and corresponding sparsity value imposed to the algorithm. On figure 1 (right), the separated fluorescence contributions of the three sources (Autofluorescence, ICG-LNP, Alexa 750) obtained are presented: the algorithm successfully unmixed the three overlapping fluorescence spectra. Our sparse NMF algorithm successfully filters fluorescence contributions of interest from in vivo spectrally resolved measurements impaired by unwanted signals. Sparsity constraints allowed getting more accurate unmixing results (previous studies on simulated data have illustrated that consequence).