Semi-blind sparse affine spectral unmixing of autofluorescence-contaminated micrographs

Abstract

Motivation: Spectral unmixing methods attempt to determine the concentrations of different fluorophores present at each pixel location in an image by analyzing a set of measured emission spectra. Unmixing algorithms have shown great promise for applications where samples contain many fluorescent labels; however, existing methods perform poorly when confronted with autofluorescence-contaminated images.

Results: We propose an unmixing algorithm designed to separate fluorophores with overlapping emission spectra from contamination by autofluorescence and background fluorescence. First, we formally define a generalization of the linear mixing model, called the affine mixture model (AMM), that specifically accounts for background fluorescence. Second, we use the AMM to derive an affine nonnegative matrix factorization method for estimating fluorophore endmember spectra from reference images. Lastly, we propose a semi-blind sparse affine spectral unmixing (SSASU) algorithm that uses knowledge of the estimated endmembers to learn the autofluorescence and background fluorescence spectra on a per-image basis. When unmixing real-world spectral images contaminated by autofluorescence, SSASU greatly improved proportion indeterminacy as compared to existing methods for a given relative reconstruction error.

Availability and implementation: The source code used for this paper was written in Julia and is available with the test data at https://github.com/brossetti/ssasu.

Fig. 1.

Comparison of seven Mean and ANMF estimated endmember spectra with fluorometer measurements. The shaded regions represent the fluorometer data, the dotted lines represent the Mean estimates and the dashed lines represent the ANMF estimates. The gray vertical lines show the wavelength where dichroic mirrors blocked the measurement of emitted light (i.e. locations of missing spectral data). Note that the missing spectral data caused some endmember estimates to deviate from the fluorometer measurements (e.g. ATTO 620)

Fig. 2.

Comparison of unmixing performance for SSASU, NLS and PoissonNMF across ten test images taken from five samples. The relative reconstruction error (top) evaluates each method’s ability to reconstruct the observed spectral image. The proportion indeterminacy (bottom) measures the non-orthogonality of the weight matrices and illustrates how well each method separates the fluorophore endmembers in the presence of autofluorescence. Both metrics range from zero (better) to one (worse)

Fig. 3.

Montage of unmixed images for NLS (top) and SSASU (bottom). Panels (A–P) show the unmixed channels for autofluorescence (A, I); S. mitis/DY-415 (B, J); S. salivarius/DY-490 (C, K); Prevotella/ATTO 520 (D, L); Veillonella/ATTO 550 (E, M); Actinomyces/Texas Red-X (F, N); Neisseriaceae/ATTO 620 (G, O); and Rothia/ATTO 655 (H, P). A larger composite view of the non-autofluorescence unmixed channels is shown for NLS in panel (Q) and for SSASU in panel (R). The scale bar in panel R indicates 10 μm. (Color version of this figure is available at Bioinformatics online.)

Fig. 4.

Comparison of the autofluorescence endmember estimated from the no-probe control reference image (gray region) to the autofluorescence endmembers learned by SSASU from each of the ten test images (colored lines). Note that none of the learned autofluorescence endmembers match the no-probe control endmember estimate. (Color version of this figure is available at Bioinformatics online.)