Hyperspectral imaging (HSI) in fluorescence-guided tumor surgery can detect and classify tumor regions invisible to the human eye. To achieve this, HSI captures the full light emission spectrum at every image pixel. Through a priori knowledge of the fluorescing substances present in the image (endmembers) and their emission spectra, the measured spectra can be unmixed to determine their relative abundance. These abundances can be used to distinguish solid tumor from infiltrating margins and healthy tissue. Prior work has determined a minimal set of viable endmember spectra, which (1) are known to be in the brain, (2) effectively fit human data, and (3) do not overfit. With these endmembers, non-negative least squares regression (NNLS) was commonly used to compute the abundances. However, one small set of basis spectra may not fit all pixels well, as HSI images are heterogeneous. Additionally, NNLS is the maximum likelihood estimator only if the measurement is normally distributed and it does not enforce sparsity, which leads to overfitting.

We propose a library of 9 endmember spectra, including PpIX (620 nm and 634 nm photostates), NADH, FAD, flavins, lipofuscin, melanin, elastin, and collagen. With these endmembers, we introduce a sparse, non-negative Poisson regression algorithm to perform the unmixing in a physics-informed manner that does not overfit.

We analyzed 555,666 HSI fluorescence spectra from 891 ex vivo measurements of biopsies of 184 patients with various brain tumors to show that a Poisson distribution models the measured data 82% better than a Gaussian in terms of the Kullback-Leibler divergence. This measurement model generated highly realistic simulated spectra with known endmember abundances. The new unmixing method was then tested on the human and simulated data and compared to four other methods. It outperforms them with 25% lower error in the computed abundances on the simulated data versus NNLS, lower reconstruction error on human data, better sparsity, and 31 times faster runtime than state of the art Poisson regression.

Our sparse, non-negative Poisson regression algorithm, utilizing 9 endmember spectra, is superior in spectral unmixing compared to existing methods, offering enhanced accuracy, reduced error rates, improved sparsity, and significantly faster runtime. This advancement holds great potential to provide more precise resection guidance, leveraging hyperspectral imaging for improved surgical outcomes.