Classification initialized hierarchical ALS-based NMF with partial sparseness constraints for fluorescence spectral unmixing

Nonnegative Matrix Factorization (NMF) is widely used in the spectral unmixing of fluorescence imaging, which decomposes the mixed fluorescence components into a set of constituent spectra and their corresponding fractional abundances. However, NMF is a nonconvex programming in the iteration process, thus the solution depends on the initial values and some constraints (such as sparseness constraints). In this paper, considering the autofluorescence (AF) and multi-target fluorophores having different characteristics of spectral and spatial distribution, we initialized NMF by using the normalized cut method, which can roughly classify all pixels into two groups: one for multi-target fluorophores and the other for AF. Therefore the spectra of multi-target fluorophores and AF can be initialized with the spectral signals in the corresponding groups. A ℓ₁-norm-based partial sparseness constraint is further imposed on the hierarchical alternating least squares (HALS)-based NMF, which only introduce partial sparsity into the abundances of multi-target fluorophores rather than autofluorescence. Based on these classification-based initialization and partial sparseness constraints for the different components of fluorescence imaging, the multi-target fluorophores are clearly discriminated from AF in the solution of NMF. By using simulated and in vivo experimental data, the performance of the proposed algorithm has been validated as the best compared with several other state-of-the-art methods.