Black David, Liquet Benoit, Di Ieva Antonio, Stummer Walter, Suero Molina Eric
Department of Electrical and Computer Engineering, University of British Columbia, Vancouver, BC, Canada.
School of Mathematical and Physical Sciences, Macquarie University, Sydney, Australia.
Biomed Opt Express. 2024 Jul 2;15(8):4406-4424. doi: 10.1364/BOE.528535. eCollection 2024 Aug 1.
Through spectral unmixing, hyperspectral imaging (HSI) in fluorescence-guided brain tumor surgery has enabled the detection and classification of tumor regions invisible to the human eye. Prior unmixing work has focused on determining a minimal set of viable fluorophore spectra known to be present in the brain and effectively reconstructing human data without overfitting. With these endmembers, non-negative least squares regression (NNLS) was commonly used to compute the abundances. However, HSI images are heterogeneous, so one small set of endmember spectra may not fit all pixels well. Additionally, NNLS is the maximum likelihood estimator only if the measurement is normally distributed, and it does not enforce sparsity, which leads to overfitting and unphysical results. In this paper, we analyzed 555666 HSI fluorescence spectra from 891 ex vivo measurements of patients with various brain tumors to show that a Poisson distribution indeed models the measured data 82% better than a Gaussian in terms of the Kullback-Leibler divergence, and that the endmember abundance vectors are sparse. With this knowledge, we introduce (1) a library of 9 endmember spectra, including PpIX (620 nm and 634 nm photostates), NADH, FAD, flavins, lipofuscin, melanin, elastin, and collagen, (2) a sparse, non-negative Poisson regression algorithm to perform physics-informed unmixing with this library without overfitting, and (3) a highly realistic spectral measurement simulation with known endmember abundances. The new unmixing method was then tested on the human and simulated data and compared to four other candidate methods. It outperforms previous methods with 25% lower error in the computed abundances on the simulated data than NNLS, lower reconstruction error on human data, better sparsity, and 31 times faster runtime than state-of-the-art Poisson regression. This method and library of endmember spectra can enable more accurate spectral unmixing to aid the surgeon better during brain tumor resection.
通过光谱解混，荧光引导脑肿瘤手术中的高光谱成像（HSI）能够检测和分类人眼不可见的肿瘤区域。先前的解混工作主要集中在确定已知存在于大脑中的一组最小可行荧光团光谱，并有效地重建人类数据而不过度拟合。利用这些端元，非负最小二乘回归（NNLS）通常用于计算丰度。然而，HSI图像是异质的，因此一组小的端元光谱可能无法很好地拟合所有像素。此外，只有在测量呈正态分布时，NNLS才是最大似然估计器，并且它不强制稀疏性，这会导致过度拟合和不符合实际的结果。在本文中，我们分析了来自891例各种脑肿瘤患者的离体测量的555666个HSI荧光光谱，结果表明，就库尔贝克-莱布勒散度而言，泊松分布对测量数据的建模效果确实比高斯分布好82%，并且端元丰度向量是稀疏的。基于这一认识，我们引入了：（1）一个包含9种端元光谱的库，包括原卟啉IX（620纳米和634纳米光态）、烟酰胺腺嘌呤二核苷酸（NADH）、黄素腺嘌呤二核苷酸（FAD）、黄素、脂褐素、黑色素、弹性蛋白和胶原蛋白；（2）一种稀疏、非负泊松回归算法，用于使用该库进行物理信息解混而不过度拟合；（3）一种具有已知端元丰度的高度逼真的光谱测量模拟。然后，在人类数据和模拟数据上对新的解混方法进行了测试，并与其他四种候选方法进行了比较。它在模拟数据上的计算丰度误差比NNLS低25%，在人类数据上的重建误差更低，稀疏性更好，运行时间比最先进的泊松回归快31倍，优于先前的方法。这种方法和端元光谱库可以实现更准确的光谱解混，在脑肿瘤切除过程中更好地帮助外科医生。
