Attenuation-corrected fluorescence spectra unmixing for spectroscopy and microscopy

Attenuation correction for confocal laser scanning microscopy and its application in chromatography

The applicability of confocal laser scanning microscopy is limited, e.g. by attenuation of the excitation and the fluorescence emission beam. As a prerequisite for further processing and analysis of the obtained microscopic images, a new method is presented for correcting this attenuation. The correction is based on beam modelling and on a differential form of the modified Beer-Lambert law. It turns out that the intensity decay can be modelled as a double convolution of the microscopic image with the intensities of the excitation semibeam and the emission beam. Under weak assumptions made for the intensities of the fluorescent radiation and the detected signal, formulas for the attenuation correction and the attenuation simulation are derived. The method traces back to that one published by Roerdink which is modified concerning a more realistic beam modelling, avoiding the so-called weak attenuation expansion and considering fluorescence excitation throughout the light cone of the excitation beam. The applicability of the method is demonstrated for synthetic examples as well as microscopic images of chromatographic beads. It is shown that the new method can be successfully applied for reconstructing the true fluorophore distribution in specimens even if the microscopic images are affected by strong attenuation. LAY DESCRIPTION: The applicability of confocal laser scanning microscopy is limited by attenuation of the excitation and the fluorescence emission beam. As a prerequisite for further processing and analysis of the obtained microscopic images, a new method is presented for correcting this attenuation. The correction is based on modeling the excitation as well as the emission beam and on a modified Beer-Lambert law for beam attenuation. The applicability of the method is demonstrated for synthetic examples as well as microscopic images of chromatographic beads. It is shown that the new method can be successfully applied for reconstructing the true fluorophore distribution in specimens even if the microscopic images are affected by strong attenuation.

Simultaneous Surface Reflectance and Fluorescence Spectra Estimation

There is widespread interest in estimating the fluorescence properties of natural materials in an image. However, the separation between reflected and fluoresced components is difficult, because it is impossible to distinguish reflected and fluoresced photons without controlling the illuminant spectrum. We show how to jointly estimate the reflectance and fluorescence from a single set of images acquired under multiple illuminants. We present a framework based on a linear approximation to the physical equations describing image formation in terms of surface spectral reflectance and fluorescence due to multiple fluorophores. We relax the non-convex, inverse estimation problem in order to jointly estimate the reflectance and fluorescence properties in a single optimization step. We provide a software implementation of the solver for our method and prior methods. We evaluate the accuracy and reliability of the method using both simulations and experimental data. To evaluate the methods experimentally we built a custom imaging system using a monochrome camera, a filter wheel with bandpass transmissive filters and a small number of light emitting diodes. We compared the methods based upon our framework with the ground truth as well as with prior methods.

Robust Non-negative Tensor Factorization, Diffeomorphic Motion Correction, and Functional Statistics to Understand Fixation in Fluorescence Microscopy

Fixation is essential for preserving cellular morphology in biomedical research. However, it may also affect spectra captured in multispectral fluorescence microscopy, impacting molecular interpretations. To investigate fixation effects on tissue, multispectral fluorescence microscopy images of pairs of samples with and without fixation are captured. Each pixel might exhibit overlapping spectra, creating a blind source separation problem approachable with linear unmixing. With multiple excitation wavelengths, unmixing is intuitively extended to tensor factorizations. Yet these approaches are limited by nonlinear effects like attenuation. Further, light exposure during image acquisition introduces subtle Brownian motion between image channels of non-fixed tissue. Finally, hypothesis testing for spectral differences due to fixation is nontrivial as retrieved spectra are paired sequential samples. To these ends, we present three contributions, (1) a novel robust non-negative tensor factorization using the β-divergence and L _2,1-norm, which decomposes the data into a low-rank multilinear and group-sparse non-multilinear tensor without making any explicit nonlinear modeling choices or assumptions on noise statistics; (2) a diffeomorphic atlas-based strategy for motion correction; (3) a non-parametric hypothesis testing framework for paired sequential data using functional principal component analysis.

Tensor decomposition of hyperspectral images to study autofluorescence in age-related macular degeneration

Autofluorescence is the emission of light by naturally occurring tissue components on the absorption of incident light. Autofluorescence within the eye is associated with several disorders, such as Age-related Macular Degeneration (AMD) which is a leading cause of central vision loss. Its pathogenesis is incompletely understood, but endogenous fluorophores in retinal tissue might play a role. Hyperspectral fluorescence microscopy of ex-vivo retinal tissue can be used to determine the fluorescence emission spectra of these fluorophores. Comparisons of spectra in healthy and diseased tissues can provide important insights into the pathogenesis of AMD. However, the spectrum from each pixel of the hyperspectral image is a superposition of spectra from multiple overlapping tissue components. As spectra cannot be negative, there is a need for a non-negative blind source separation model to isolate individual spectra. We propose a tensor formulation by leveraging multiple excitation wavelengths to excite the tissue sample. Arranging images from different excitation wavelengths as a tensor, a non-negative tensor decomposition can be performed to recover a provably unique low-rank model with factors representing emission and excitation spectra of these materials and corresponding abundance maps of autofluorescent substances in the tissue sample. We iteratively impute missing values common in fluorescence measurements using Expectation-Maximization and use L2 regularization to reduce ill-posedness. Further, we present a framework for performing group hypothesis testing on hyperspectral images, finding significant differences in spectra between AMD and control groups in the peripheral macula. In the absence of ground truth, i.e. molecular identification of fluorophores, we provide a rigorous validation of chosen methods on both synthetic and real images where fluorescence spectra are known. These methodologies can be applied to the study of other pathologies presenting autofluorescence that can be captured by hyperspectral imaging.