Unmixing biological fluorescence image data with sparse and low-rank Poisson regression

Abstract

Motivation: Multispectral biological fluorescence microscopy has enabled the identification of multiple targets in complex samples. The accuracy in the unmixing result degrades (i) as the number of fluorophores used in any experiment increases and (ii) as the signal-to-noise ratio in the recorded images decreases. Further, the availability of prior knowledge regarding the expected spatial distributions of fluorophores in images of labeled cells provides an opportunity to improve the accuracy of fluorophore identification and abundance.

Results: We propose a regularized sparse and low-rank Poisson regression unmixing approach (SL-PRU) to deconvolve spectral images labeled with highly overlapping fluorophores which are recorded in low signal-to-noise regimes. First, SL-PRU implements multipenalty terms when pursuing sparseness and spatial correlation of the resulting abundances in small neighborhoods simultaneously. Second, SL-PRU makes use of Poisson regression for unmixing instead of least squares regression to better estimate photon abundance. Third, we propose a method to tune the SL-PRU parameters involved in the unmixing procedure in the absence of knowledge of the ground truth abundance information in a recorded image. By validating on simulated and real-world images, we show that our proposed method leads to improved accuracy in unmixing fluorophores with highly overlapping spectra.

Availability and implementation: The source code used for this article was written in MATLAB and is available with the test data at https://github.com/WANGRUOGU/SL-PRU.

Figure 1.

A hyperspectral data cube and spectral intensity information at each pixel with a generalized biological image, in which most foreground pixels record fluorescent signal from only one cell but some pixels record overlapped signals from two or more cells

Figure 2.

A 3 × 3 window unmixed into the product of its endmember and abundance matrices

Figure 3.

Graphical representation of simulated image pixels that contain two colocalized endmembers, either AF514 and RRX [highly uncorrelated endmembers (top row)] or AF555 and RRX [highly correlated endmembers (bottom row)]. In each row, the “Truth” matrix represents the ground truth starting the simulation. Subsequent matrices represent the results of estimated abundances obtained from each of the unmixing methods that we considered. For each matrix, the 13 rows represent the 13 different endmembers used in the simulation and each column represents an independent pixel with varying intensity, scaled from 0 to 1. The color represents the mean abundance measure for each fluorophore from 1000 simulations of the same ground truth model after applying Poisson noise with SNR $=5$ to each pixel

Figure 4.

Averages of RMSEs of the abundances estimated by each of the unmixing methods that we considered from simulated images that contain colocalized AF514 and RRX with Poisson noise and SNR of 2 to 10

Figure 5.

Averages of RMSEs of the abundances estimated by each of the unmixing methods that we considered from simulated images that contain colocalized AF555 and RRX with Poisson noise and SNR of 2 to 10

Figure 6.

Qualitative comparison of least squares and SL-PRU unmixing on a real biological sample. (A–F) Multi-spectral image of a dental plaque smear hedgehog structure after (A–C) least squares unmixing and (D–F) SL-PRU unmixing. Dashed boxes in (A) and (B) and in (C) and (D) indicate zoom area in C and D, and E and F, respectively. Scale bars equal 100 µm (D), 25 µm, (E), and 10 µm (F)

Figure 7.

Quantitative comparison of mean circularity measurement per cell for two coccoid-shaped cells in the plaque structure: Streptococcus (A) and Veillonella (B). Light grey bars = results from least squares unmixing, dark grey bars = results from SL-PU. Error bars represent 95% confidence intervals. ****P < .001 Welch’s t-test