Rehaussement du signal de parole par EMD et opérateur de Teager-Kaiser

The authors would like to thank Professor Mohamed Bahoura from Universite de Quebec a Rimouski for fruitful discussions on time adaptive thresholdingIn this paper a speech denoising strategy based on time adaptive thresholding of intrinsic modes functions (IMFs) of the signal, extracted by empirical mode decomposition (EMD), is introduced. The denoised signal is reconstructed by the superposition of its adaptive thresholded IMFs. Adaptive thresholds are estimated using the Teager–Kaiser energy operator (TKEO) of signal IMFs. More precisely, TKEO identifies the type of frame by expanding differences between speech and non-speech frames in each IMF. Based on the EMD, the proposed speech denoising scheme is a fully data-driven approach. The method is tested on speech signals with different noise levels and the results are compared to EMD-shrinkage and wavelet transform (WT) coupled with TKEO. Speech enhancement performance is evaluated using output signal to noise ratio (SNR) and perceptual evaluation of speech quality (PESQ) measure. Based on the analyzed speech signals, the proposed enhancement scheme performs better than WT-TKEO and EMD-shrinkage approaches in terms of output SNR and PESQ. The noise is greatly reduced using time-adaptive thresholding than universal thresholding. The study is limited to signals corrupted by additive white Gaussian noise

Adaptive Thresholding for Sparse Covariance Matrix Estimation

In this paper we consider estimation of sparse covariance matrices and propose a thresholding procedure which is adaptive to the variability of individual entries. The estimators are fully data driven and enjoy excellent performance both theoretically and numerically. It is shown that the estimators adaptively achieve the optimal rate of convergence over a large class of sparse covariance matrices under the spectral norm. In contrast, the commonly used universal thresholding estimators are shown to be sub-optimal over the same parameter spaces. Support recovery is also discussed. The adaptive thresholding estimators are easy to implement. Numerical performance of the estimators is studied using both simulated and real data. Simulation results show that the adaptive thresholding estimators uniformly outperform the universal thresholding estimators. The method is also illustrated in an analysis on a dataset from a small round blue-cell tumors microarray experiment. A supplement to this paper which contains additional technical proofs is available online.Comment: To appear in Journal of the American Statistical Associatio

Adaptive covariance matrix estimation through block thresholding

Estimation of large covariance matrices has drawn considerable recent attention, and the theoretical focus so far has mainly been on developing a minimax theory over a fixed parameter space. In this paper, we consider adaptive covariance matrix estimation where the goal is to construct a single procedure which is minimax rate optimal simultaneously over each parameter space in a large collection. A fully data-driven block thresholding estimator is proposed. The estimator is constructed by carefully dividing the sample covariance matrix into blocks and then simultaneously estimating the entries in a block by thresholding. The estimator is shown to be optimally rate adaptive over a wide range of bandable covariance matrices. A simulation study is carried out and shows that the block thresholding estimator performs well numerically. Some of the technical tools developed in this paper can also be of independent interest.Comment: Published in at http://dx.doi.org/10.1214/12-AOS999 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Adaptive Nonparametric Regression on Spin Fiber Bundles

The construction of adaptive nonparametric procedures by means of wavelet thresholding techniques is now a classical topic in modern mathematical statistics. In this paper, we extend this framework to the analysis of nonparametric regression on sections of spin fiber bundles defined on the sphere. This can be viewed as a regression problem where the function to be estimated takes as its values algebraic curves (for instance, ellipses) rather than scalars, as usual. The problem is motivated by many important astrophysical applications, concerning for instance the analysis of the weak gravitational lensing effect, i.e. the distortion effect of gravity on the images of distant galaxies. We propose a thresholding procedure based upon the (mixed) spin needlets construction recently advocated by Geller and Marinucci (2008,2010) and Geller et al. (2008,2009), and we investigate their rates of convergence and their adaptive properties over spin Besov balls.Comment: 40 page