Abstract
BackgroundNonnegative matrix factorization (NMF) has been used in blind fluorescence unmixing for multispectral in-vivo fluorescence imaging, which decomposes a mixed source data into a set of constituent fluorescence spectra and corresponding concentrations. However, most classical NMF algorithms have ill convergence problems and they always fail to unmix multiple fluorescent targets from background autofluorescence for the sparse acquisition of multispectral fluorescence imaging, which introduces incomplete measurements and severe discontinuities in multispectral fluorescence emissions across the multiple spectral bands. MethodsObserving the spatial distinction between the diffusive autofluorescence and the sparse fluorescent targets, we propose to separate the mixed sparse multispectral data into equality constrained two-hierarchical updating within NMF framework by dividing the concentration matrix of entire endmembers into two hierarchies: the fluorescence targets and the background autofluorescence. Specifically, when updating concentrations of multiple fluorescent targets in the two-hierarchical NMF, we assume that the concentration of autofluorescence is fixed and known, and vice versa. Furthermore, a sparsity constraint is imposed on the concentration matrix components of fluorescence targets only.ResultsSynthetic data sets, in vivo fluorescence imaging data are employed to demonstrate and validate the performance of our approach. The proposed algorithm can achieve more satisfying results of spectral unmixing and autofluorescence removal compared to other state-of-the-art methods, especially for the sparse multispectral fluorescence imaging.ConclusionsThe proposed algorithm can successfully tackle the sparse acquisition and ill-posed problems in the NMF-based fluorescence unmixing through equality constraint along with partial sparsity constraint during two-hierarchical NMF optimization, at which fixing sparsity constrained target fluorescence can make the update of autofluorescence as accurate as possible and vice versa.
Highlights
Nonnegative matrix factorization (NMF) has been used in blind fluorescence unmixing for multispectral in-vivo fluorescence imaging, which decomposes a mixed source data into a set of constituent fluorescence spectra and corresponding concentrations
Before we dig into some fluorescence unmixing methods, it will help us to have a general understanding of the following observations in fluorescence imaging: first, due to in-vivo fluorescence imaging measuring the diffuse radiance from the surface of scattering animal tissue after the fluorescent light transport in tissues, a fluorophore inside animal tissue might make a significant contribution to a cloud of neighboring pixels instead of only the pixel geometrically associated with it, such that the quantity C for multiple fluorophores represents the signal distribution of these multiple fluorophores instead of the concentrations of fluorophores in the pixel [3]; second, the emitted fluorescent light travel in diffusive tissues can result in the decreasing intensity and spectral distortions
Experimental results with synthetic data we define a simulated experiment to quantitatively evaluate the performance of two-hierarchical NMF (thNMF) algorithm compared to other four classic spectral unmixing algorithms: multivariate curve resolution-alternating least squares (MCR-ALS) [3], hierarchical alternating least squares (HALS)-based NMF with l1-norm constraint on C (NMFl1) [24], NMF with sparsity constraints on C (NMFsc) [28], sparse NMF [4]
Summary
Nonnegative matrix factorization (NMF) has been used in blind fluorescence unmixing for multispectral in-vivo fluorescence imaging, which decomposes a mixed source data into a set of constituent fluorescence spectra and corresponding concentrations. To solve the overlapping problem in fluorescence imaging, spectral unmixing (SUM) is used to decompose the mixed spectra data D into a product of pure spectral signatures S, i.e., endmembers, and corresponding concentrations C (or abundances, mixing weights), representing the contribution to the observed fluorescence radiance from the corresponding endmember. By returning separated pure fluorescence contribution data, the SUM method gives contrastenhanced [6] signal distribution of each target fluorophore in 2D planar imaging to enable comparing fluorescence sources at similar imaging conditions and comparable depth, and presents the possibility to perform accurate fluorescence tomographic reconstructions confirming the 3D position of marked samples
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