Information theoretic analysis of hyperspectral imaging systems with applications to fluorescence microscopy.

Sripad Ram

doi:10.1364/boe.10.003380

Abstract

We present a general stochastic model for hyperspectral imaging data and derive analytical expressions for the Fisher information matrix for the underlying spectral unmixing problem. We investigate the linear mixing model as a special case and define a linear unmixing performance bound by using the Cramer-Rao inequality. As an application, we consider fluorescence imaging and show how the performance bound provides a spectral resolution limit that predicts how accurately a pair of spectrally similar fluorescent labels can be spectrally unmixed. We also report a novel result that shows how the spectral resolution limit can be overcome by exploiting the phenomenon of anti-Stokes shift fluorescence. In addition, we investigate how photon statistics, channel addition and channel splitting affect the performance bound. Finally by using the performance bound as a benchmark, we compare the performance of the least squares and the maximum likelihood estimators for spectral unmixing. For the imaging conditions tested here, our analysis shows that both estimators are unbiased and that the standard deviation of the maximum likelihood estimator is consistently closer to the performance bound than that of the least squares estimator. The results presented here are based on broad assumptions regarding the underlying data model and are applicable to hyperspectral data acquired with point detectors, sCMOS, CCD and EMCCD imaging detectors.

Highlights

Hyperspectral imaging represents a broad class of techniques that capture spectral and spatial data from the object of interest
Bound for the ith label at the kth pixel in the output image cube is defined as δk,i = [I−k 1(θ)]ii, θ ∈ Θ, and the Linear Unmixing Performance (LUP) bound for the best case scenario is defined as δkbc,i = [Gk−1(θ)]ii, where Ik(θ) = AT Gk(θ)A, A denotes the mixing matrix and Gk(θ) is given by 9, for θ ∈ Θ and k = 1, . . . , Np
An important question that arises in hyperspectral imaging applications concerns with how accurately two spectrally overlapping fluorescent labels can be discerned from the acquired data

Summary

Introduction

Hyperspectral imaging represents a broad class of techniques that capture spectral and spatial data from the object of interest. Hyperspectral imaging can be carried out either with a confocal ([1], [2], [3]) or a linescanning ([4]) microscope that has spectral detection capability It can be carried out on a widefield microscope by using either narrowband excitation and emission filters ([5], [6], [7], [8]) or by using an electronically controlled liquid crystal tunable filter ([9], [10]). Common to all these techniques is the underlying hyperspectral data which consists of a sequence of 2D images acquired at different spectral windows. Given the hyperspectral data, the goal is to estimate the relative abundance (typically represented in photon counts) of the different labels at each pixel, and this is referred to as the spectral unmixing problem (Fig. 1C)

Methods

Results

Conclusion