Unmixing Biological Fluorescence Image Data with Sparse and Low-Rank Poisson Regression

Multispectral biological fluorescence microscopy has enabled the identification of multiple targets in complex samples. The accuracy in the unmixing result degrades (1) as the number of fluorophores used in any experiment increases and (2) 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. We propose a regularized sparse and low-rank Poisson unmixing approach (SL-PRU) to deconvolve spectral images labeled with highly overlapping fluorophores which are recorded in low signal-to-noise regimes. Firstly, SL-PRU implements multi-penalty terms when pursuing sparseness and spatial correlation of the resulting abundances in small neighborhoods simultaneously. Secondly, SL-PRU makes use of Poisson regression for unmixing instead of least squares regression to better estimate photon abundance. Thirdly, 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.

多光谱生物荧光显微镜使得在复杂样本中识别多个目标成为可能。随着任何实验中使用的荧光团数量增加以及所记录图像的信噪比降低，解混结果的准确性会下降。此外，关于标记细胞图像中荧光团预期空间分布的先验知识的可用性为提高荧光团识别和丰度的准确性提供了机会。我们提出一种正则化稀疏低秩泊松解混方法（SL - PRU），用于对在低信噪比条件下记录的、用高度重叠荧光团标记的光谱图像进行去卷积。首先，SL - PRU在同时追求小邻域内所得丰度的稀疏性和空间相关性时实施多惩罚项。其次，SL - PRU利用泊松回归而非最小二乘回归进行解混，以更好地估计光子丰度。第三，我们提出一种在缺乏所记录图像中真实丰度信息的情况下调整解混过程中涉及的SL - PRU参数的方法。通过对模拟图像和真实世界图像进行验证，我们表明我们提出的方法提高了对具有高度重叠光谱的荧光团进行解混的准确性。