The three dimensional power spectrum of dark and luminous matter from the VIRMOS-DESCART cosmic shear survey

We present the first optimal power spectrum estimation and three dimensional deprojections for the dark and luminous matter and their cross correlations. The results are obtained using a new optimal fast estimator (Pen 2003) deprojected using minimum variance and SVD techniques. We show the resulting 3-D power spectra for dark matter and galaxies, and their covariance for the VIRMOS-DESCART weak lensing shear and galaxy data. The survey is most sensitive to nonlinear scales k_NL ~ 1 h Mpc^-1. On these scales, our 3-D power spectrum of dark matter is in good agreement with the RCS 3-D power spectrum found by (Hoekstra et al 2002). Our galaxy power is similar to that found by the 2MASS survey, and larger than that of SDSS, APM and RCS, consistent with the expected difference in galaxy population. We find an average bias b=1.24+/-0.18 for the I selected galaxies, and a cross correlation coefficient r=0.75+/-0.23. Together with the power spectra, these results optimally encode the entire two point information about dark matter and galaxies, including galaxy-galaxy lensing. We address some of the implications regarding galaxy halos and mass-to-light ratios. The best fit ``halo'' parameter h=r/b=0.57+/-0.16, suggesting that dynamical masses estimated using galaxies systematically underestimate total mass. Ongoing surveys, such as the Canada-France-Hawaii-Telescope-Legacy survey will significantly improve on the dynamic range, and future photometric redshift catalogs will allow tomography along the same principles.Comment: 17 pages, 19 figures, submitted to mnra

Robust Estimation of Non-Stationary Noise Power Spectrum for Speech Enhancement

International audienceWe propose a novel method for noise power spectrum estimation in speech enhancement. This method called extended-DATE (E-DATE) extends the d-dimensional amplitude trimmed estimator (DATE), originally introduced for additive white gaussian noise power spectrum estimation, to the more challenging scenario of non-stationary noise. The key idea is that, in each frequency bin and within a sufficiently short time period, the noise instantaneous power spectrum can be considered as approximately constant and estimated as the variance of a complex gaussian noise process possibly observed in the presence of the signal of interest. The proposed method relies on the fact that the Short-Time Fourier Transform (STFT) of noisy speech signals is sparse in the sense that transformed speech signals can be represented by a relatively small number of coefficients with large amplitudes in the time-frequency domain. The E-DATE estimator is robust in that it does not require prior information about the signal probability distribution except for the weak-sparseness property. In comparison to other state-of-the-art methods, the E-DATE is found to require the smallest number of parameters (only two). The performance of the proposed estimator has been evaluated in combination with noise reduction and compared to alternative methods. This evaluation involves objective as well as pseudo-subjective criteria

Approximating the Spectrum of a Graph

The spectrum of a network or graph $G=(V,E)$ with adjacency matrix $A$, consists of the eigenvalues of the normalized Laplacian $L= I - D^{-1/2} A D^{-1/2}$. This set of eigenvalues encapsulates many aspects of the structure of the graph, including the extent to which the graph posses community structures at multiple scales. We study the problem of approximating the spectrum $\lambda = (\lambda_1,\dots,\lambda_{|V|})$, $0 \le \lambda_1,\le \dots, \le \lambda_{|V|}\le 2$ of $G$ in the regime where the graph is too large to explicitly calculate the spectrum. We present a sublinear time algorithm that, given the ability to query a random node in the graph and select a random neighbor of a given node, computes a succinct representation of an approximation $\widetilde \lambda = (\widetilde \lambda_1,\dots,\widetilde \lambda_{|V|})$, $0 \le \widetilde \lambda_1,\le \dots, \le \widetilde \lambda_{|V|}\le 2$ such that $\|\widetilde \lambda - \lambda\|_1 \le \epsilon |V|$. Our algorithm has query complexity and running time $exp(O(1/\epsilon))$, independent of the size of the graph, $|V|$. We demonstrate the practical viability of our algorithm on 15 different real-world graphs from the Stanford Large Network Dataset Collection, including social networks, academic collaboration graphs, and road networks. For the smallest of these graphs, we are able to validate the accuracy of our algorithm by explicitly calculating the true spectrum; for the larger graphs, such a calculation is computationally prohibitive. In addition we study the implications of our algorithm to property testing in the bounded degree graph model