Towards unsupervised fluorescence lifetime imaging using low dimensional variable projection.

Analyzing large fluorescence lifetime imaging (FLIM) data is becoming overwhelming; the latest FLIM systems easily produce massive amounts of data, making an efficient analysis more challenging than ever. In this paper we propose the combination of a custom-fit variable projection method, with a Laguerre expansion based deconvolution, to analyze bi-exponential data obtained from time-domain FLIM systems. Unlike nonlinear least squares methods, which require a suitable initial guess from an experienced researcher, the new method is free from manual interventions and hence can support automated analysis. Monte Carlo simulations are carried out on synthesized FLIM data to demonstrate the performance compared to other approaches. The performance is also illustrated on real-life FLIM data obtained from the study of autofluorescence of daisy pollen and the endocytosis of gold nanorods (GNRs) in living cells. In the latter, the fluorescence lifetimes of the GNRs are much shorter than the full width at half maximum of the instrument response function. Overall, our proposed method contains simple steps and shows great promise in realising automated FLIM analysis of large data sets.

Sparse reconstruction of correlated multichannel activity.

Parametric methods for modeling sinusoidal signals with line spectra have been studied for decades. In general, these methods start by representing each sinusoidal component by means of two complex exponential functions, thereby doubling the number of unknown parameters. Recently, a Hankel-plus-Toeplitz matrix pencil method was proposed which directly models sinusoidal signals with discrete spectral content. Compared to its counterpart, which uses a Hankel matrix pencil, it halves the required number of time-domain samples and reduces the size of the involved linear systems. The aim of this paper is twofold. Firstly, to show that this Hankel-plus-Toeplitz matrix pencil also applies to continuous spectra. Secondly, to explore its use in the reconstruction of real-life signals. Promising preliminary results in the reconstruction of correlated multichannel electroencephalographic (EEG) activity are presented. A principal component analysis preprocessing step is carried out to exploit the redundancy in the channel domain. Then the reduced signal representation is successfully reconstructed from fewer samples using the Hankel-plus-Toeplitz matrix pencil. The obtained results encourage the future development of this matrix pencil method along the lines of well-established spectral analysis methods.

Rational BRDF.

Over the last two decades, much effort has been devoted to accurately measuring Bidirectional Reflectance Distribution Functions (BRDFs) of real-world materials and to use efficiently the resulting data for rendering. Because of their large size, it is difficult to use directly measured BRDFs for real-time applications, and fitting the most sophisticated analytical BRDF models is still a complex task. In this paper, we introduce Rational BRDF, a general-purpose and efficient representation for arbitrary BRDFs, based on Rational Functions (RFs). Using an adapted parametrization, we demonstrate how Rational BRDFs offer 1) a more compact and efficient representation using low-degree RFs, 2) an accurate fitting of measured materials with guaranteed control of the residual error, and 3) efficient importance sampling by applying the same fitting process to determine the inverse of the Cumulative Distribution Function (CDF) generated from the BRDF for use in Monte-Carlo rendering.