Decorrelation of Neutral Vector Variables: Theory and Applications

In this paper, we propose novel strategies for neutral vector variable decorrelation. Two fundamental invertible transformations, namely serial nonlinear transformation and parallel nonlinear transformation, are proposed to carry out the decorrelation. For a neutral vector variable, which is not multivariate Gaussian distributed, the conventional principal component analysis (PCA) cannot yield mutually independent scalar variables. With the two proposed transformations, a highly negatively correlated neutral vector can be transformed to a set of mutually independent scalar variables with the same degrees of freedom. We also evaluate the decorrelation performances for the vectors generated from a single Dirichlet distribution and a mixture of Dirichlet distributions. The mutual independence is verified with the distance correlation measurement. The advantages of the proposed decorrelation strategies are intensively studied and demonstrated with synthesized data and practical application evaluations

Compressive Source Separation: Theory and Methods for Hyperspectral Imaging

With the development of numbers of high resolution data acquisition systems and the global requirement to lower the energy consumption, the development of efficient sensing techniques becomes critical. Recently, Compressed Sampling (CS) techniques, which exploit the sparsity of signals, have allowed to reconstruct signal and images with less measurements than the traditional Nyquist sensing approach. However, multichannel signals like Hyperspectral images (HSI) have additional structures, like inter-channel correlations, that are not taken into account in the classical CS scheme. In this paper we exploit the linear mixture of sources model, that is the assumption that the multichannel signal is composed of a linear combination of sources, each of them having its own spectral signature, and propose new sampling schemes exploiting this model to considerably decrease the number of measurements needed for the acquisition and source separation. Moreover, we give theoretical lower bounds on the number of measurements required to perform reconstruction of both the multichannel signal and its sources. We also proposed optimization algorithms and extensive experimentation on our target application which is HSI, and show that our approach recovers HSI with far less measurements and computational effort than traditional CS approaches.Comment: 32 page

Computing aerodynamic sound using advanced statistical turbulence theories

It is noted that the calculation of turbulence-generated aerodynamic sound requires knowledge of the spatial and temporal variation of Q sub ij (xi sub k, tau), the two-point, two-time turbulent velocity correlations. A technique is presented to obtain an approximate form of these correlations based on closure of the Reynolds stress equations by modeling of higher order terms. The governing equations for Q sub ij are first developed for a general flow. The case of homogeneous, stationary turbulence in a unidirectional constant shear mean flow is then assumed. The required closure form for Q sub ij is selected which is capable of qualitatively reproducing experimentally observed behavior. This form contains separation time dependent scale factors as parameters and depends explicitly on spatial separation. The approximate forms of Q sub ij are used in the differential equations and integral moments are taken over the spatial domain. The velocity correlations are used in the Lighthill theory of aerodynamic sound by assuming normal joint probability

Wavelet Domain Image Separation

In this paper, we consider the problem of blind signal and image separation using a sparse representation of the images in the wavelet domain. We consider the problem in a Bayesian estimation framework using the fact that the distribution of the wavelet coefficients of real world images can naturally be modeled by an exponential power probability density function. The Bayesian approach which has been used with success in blind source separation gives also the possibility of including any prior information we may have on the mixing matrix elements as well as on the hyperparameters (parameters of the prior laws of the noise and the sources). We consider two cases: first the case where the wavelet coefficients are assumed to be i.i.d. and second the case where we model the correlation between the coefficients of two adjacent scales by a first order Markov chain. This paper only reports on the first case, the second case results will be reported in a near future. The estimation computations are done via a Monte Carlo Markov Chain (MCMC) procedure. Some simulations show the performances of the proposed method. Keywords: Blind source separation, wavelets, Bayesian estimation, MCMC Hasting-Metropolis algorithm.Comment: Presented at MaxEnt2002, the 22nd International Workshop on Bayesian and Maximum Entropy methods (Aug. 3-9, 2002, Moscow, Idaho, USA). To appear in Proceedings of American Institute of Physic

Generation of Pure-State Single-Photon Wavepackets by Conditional Preparation Based on Spontaneous Parametric Downconversion

We study the conditional preparation of single photons based on parametric downconversion, where the detection of one photon from a given pair heralds the existence of a single photon in the conjugate mode. We derive conditions on the modal characteristics of the photon pairs, which ensure that the conditionally prepared single photons are quantum-mechanically pure. We propose specific experimental techniques that yield photon pairs ideally suited for single-photon conditional preparation.Comment: 14 pages, 6 figure

On the rate-distortion performance and computational efficiency of the Karhunen-Loeve transform for lossy data compression

We examine the rate-distortion performance and computational complexity of linear transforms for lossy data compression. The goal is to better understand the performance/complexity tradeoffs associated with using the Karhunen-Loeve transform (KLT) and its fast approximations. Since the optimal transform for transform coding is unknown in general, we investigate the performance penalties associated with using the KLT by examining cases where the KLT fails, developing a new transform that corrects the KLT's failures in those examples, and then empirically testing the performance difference between this new transform and the KLT. Experiments demonstrate that while the worst KLT can yield transform coding performance at least 3 dB worse than that of alternative block transforms, the performance penalty associated with using the KLT on real data sets seems to be significantly smaller, giving at most 0.5 dB difference in our experiments. The KLT and its fast variations studied here range in complexity requirements from O(n^2) to O(n log n) in coding vectors of dimension n. We empirically investigate the rate-distortion performance tradeoffs associated with traversing this range of options. For example, an algorithm with complexity O(n^3/2) and memory O(n) gives 0.4 dB performance loss relative to the full KLT in our image compression experiment

Understanding Slow Feature Analysis: A Mathematical Framework

Slow feature analysis is an algorithm for unsupervised learning of invariant representations from data with temporal correlations. Here, we present a mathematical analysis of slow feature analysis for the case where the input-output functions are not restricted in complexity. We show that the optimal functions obey a partial differential eigenvalue problem of a type that is common in theoretical physics. This analogy allows the transfer of mathematical techniques and intuitions from physics to concrete applications of slow feature analysis, thereby providing the means for analytical predictions and a better understanding of simulation results. We put particular emphasis on the situation where the input data are generated from a set of statistically independent sources.\ud The dependence of the optimal functions on the sources is calculated analytically for the cases where the sources have Gaussian or uniform distribution