Spectral Separation of Quantum Dots within Tissue Equivalent Phantom Using Linear Unmixing Methods in Multispectral Fluorescence Reflectance Imaging

Introduction Non-invasive Fluorescent Reflectance Imaging (FRI) is used for accessing physiological and molecular processes in biological media. The aim of this article is to separate the overlapping emission spectra of quantum dots within tissue-equivalent phantom using SVD, Jacobi SVD, and NMF methods in the FRI mode. Materials and Methods In this article, a tissue-like phantom and an optical setup in reflectance mode were developed. The algorithm of multispectral imaging method was then written in Matlab environment. The setup included the diode-pumped solid-state lasers at 479 nm, 533 nm, and 798 nm, achromatic telescopic, mirror, high pass and low pass filters, and EMCCD camera. The FRI images were acquired by a CCD camera using band pass filter centered at 600 nm and high pass max at 615 nm for the first region and high pass filter max at 810 nm for the second region. The SVD and Jacobi SVD algorithms were written in Matlab environment and compared with a Non-negative Matrix Factorization (NMF) and applied to the obtained images. Results PSNR, SNR, CNR of SVD, and NMF methods were obtained as 39 dB, 30.1 dB, and 0.7 dB, respectively. The results showed that the difference of Jacobi SVD PSNR with PSNR of NMF and modified NMF algorithm was significant (p<0.0001). The statistical results showed that the Jacobi SVD was more accurate than modified NMF. Conclusion In this study, the Jacobi SVD was introduced as a powerful method for obtaining the unmixed FRI images. An experimental evaluation of the algorithm will be done in the near future

Scalable Recommendation with Poisson Factorization

We develop a Bayesian Poisson matrix factorization model for forming recommendations from sparse user behavior data. These data are large user/item matrices where each user has provided feedback on only a small subset of items, either explicitly (e.g., through star ratings) or implicitly (e.g., through views or purchases). In contrast to traditional matrix factorization approaches, Poisson factorization implicitly models each user's limited attention to consume items. Moreover, because of the mathematical form of the Poisson likelihood, the model needs only to explicitly consider the observed entries in the matrix, leading to both scalable computation and good predictive performance. We develop a variational inference algorithm for approximate posterior inference that scales up to massive data sets. This is an efficient algorithm that iterates over the observed entries and adjusts an approximate posterior over the user/item representations. We apply our method to large real-world user data containing users rating movies, users listening to songs, and users reading scientific papers. In all these settings, Bayesian Poisson factorization outperforms state-of-the-art matrix factorization methods

Multichannel high resolution NMF for modelling convolutive mixtures of non-stationary signals in the time-frequency domain

Several probabilistic models involving latent components have been proposed for modeling time-frequency (TF) representations of audio signals such as spectrograms, notably in the nonnegative matrix factorization (NMF) literature. Among them, the recent high-resolution NMF (HR-NMF) model is able to take both phases and local correlations in each frequency band into account, and its potential has been illustrated in applications such as source separation and audio inpainting. In this paper, HR-NMF is extended to multichannel signals and to convolutive mixtures. The new model can represent a variety of stationary and non-stationary signals, including autoregressive moving average (ARMA) processes and mixtures of damped sinusoids. A fast variational expectation-maximization (EM) algorithm is proposed to estimate the enhanced model. This algorithm is applied to piano signals, and proves capable of accurately modeling reverberation, restoring missing observations, and separating pure tones with close frequencies

Hyperspectral Unmixing Overview: Geometrical, Statistical, and Sparse Regression-Based Approaches

Imaging spectrometers measure electromagnetic energy scattered in their instantaneous field view in hundreds or thousands of spectral channels with higher spectral resolution than multispectral cameras. Imaging spectrometers are therefore often referred to as hyperspectral cameras (HSCs). Higher spectral resolution enables material identification via spectroscopic analysis, which facilitates countless applications that require identifying materials in scenarios unsuitable for classical spectroscopic analysis. Due to low spatial resolution of HSCs, microscopic material mixing, and multiple scattering, spectra measured by HSCs are mixtures of spectra of materials in a scene. Thus, accurate estimation requires unmixing. Pixels are assumed to be mixtures of a few materials, called endmembers. Unmixing involves estimating all or some of: the number of endmembers, their spectral signatures, and their abundances at each pixel. Unmixing is a challenging, ill-posed inverse problem because of model inaccuracies, observation noise, environmental conditions, endmember variability, and data set size. Researchers have devised and investigated many models searching for robust, stable, tractable, and accurate unmixing algorithms. This paper presents an overview of unmixing methods from the time of Keshava and Mustard's unmixing tutorial [1] to the present. Mixing models are first discussed. Signal-subspace, geometrical, statistical, sparsity-based, and spatial-contextual unmixing algorithms are described. Mathematical problems and potential solutions are described. Algorithm characteristics are illustrated experimentally.Comment: This work has been accepted for publication in IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensin

Bayesian orthogonal component analysis for sparse representation

This paper addresses the problem of identifying a lower dimensional space where observed data can be sparsely represented. This under-complete dictionary learning task can be formulated as a blind separation problem of sparse sources linearly mixed with an unknown orthogonal mixing matrix. This issue is formulated in a Bayesian framework. First, the unknown sparse sources are modeled as Bernoulli-Gaussian processes. To promote sparsity, a weighted mixture of an atom at zero and a Gaussian distribution is proposed as prior distribution for the unobserved sources. A non-informative prior distribution defined on an appropriate Stiefel manifold is elected for the mixing matrix. The Bayesian inference on the unknown parameters is conducted using a Markov chain Monte Carlo (MCMC) method. A partially collapsed Gibbs sampler is designed to generate samples asymptotically distributed according to the joint posterior distribution of the unknown model parameters and hyperparameters. These samples are then used to approximate the joint maximum a posteriori estimator of the sources and mixing matrix. Simulations conducted on synthetic data are reported to illustrate the performance of the method for recovering sparse representations. An application to sparse coding on under-complete dictionary is finally investigated.Comment: Revised version. Accepted to IEEE Trans. Signal Processin

Sound Source Separation

This is the author's accepted pre-print of the article, first published as G. Evangelista, S. Marchand, M. D. Plumbley and E. Vincent. Sound source separation. In U. Zölzer (ed.), DAFX: Digital Audio Effects, 2nd edition, Chapter 14, pp. 551-588. John Wiley & Sons, March 2011. ISBN 9781119991298. DOI: 10.1002/9781119991298.ch14file: Proof:e\EvangelistaMarchandPlumbleyV11-sound.pdf:PDF owner: markp timestamp: 2011.04.26file: Proof:e\EvangelistaMarchandPlumbleyV11-sound.pdf:PDF owner: markp timestamp: 2011.04.2

Numerical methods for computing Casimir interactions

We review several different approaches for computing Casimir forces and related fluctuation-induced interactions between bodies of arbitrary shapes and materials. The relationships between this problem and well known computational techniques from classical electromagnetism are emphasized. We also review the basic principles of standard computational methods, categorizing them according to three criteria---choice of problem, basis, and solution technique---that can be used to classify proposals for the Casimir problem as well. In this way, mature classical methods can be exploited to model Casimir physics, with a few important modifications.Comment: 46 pages, 142 references, 5 figures. To appear in upcoming Lecture Notes in Physics book on Casimir Physic