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Zozor S.,Grenoble Laboratory of Images | Vignat C.,University of Marne-la-Vallee | Vignat C.,University Paris - Sud
IEEE Transactions on Signal Processing | Year: 2010

The purpose of this paper is to revisit the denoising problem of a multivariate elliptically symmetric random vector corrupted by a multivariate elliptically symmetric noise. The investigation begins with a review of multivariate elliptically distributed random vectors and of their basic but important properties. A focus is made on the Gaussian scale mixtures, a subclass of the elliptical distributions. In the second part, the denoising problem is revisited in this elliptical context following two classical directions: the minimum mean square error and the maximum a posteriori estimation approaches. Although subject to some restrictions, this investigation extends the two recent studies by Alecu et al. and Selesnick. The practical use of the proposed estimators and some possible special behaviors are then discussed through various illustrative examples. © 2009 IEEE. Source

Ben Ali F.,National Engineering School of Tunis | Ben Ali F.,Grenoble Laboratory of Images | Girin L.,Grenoble Laboratory of Images | Larbi S.D.,National Engineering School of Tunis
20th International Congress on Acoustics 2010, ICA 2010 - Incorporating Proceedings of the 2010 Annual Conference of the Australian Acoustical Society | Year: 2010

The harmonic plus noise model (HNM) is widely used for spectral modelling of sounds that combine harmonic and noise components, like speech signals and signals produced by a series of musical instruments. A simplified and efficient version of the HNM, developed by Stylianou et al., splits the frequency band of the signal into two bands: a harmonic part for low frequencies and a noise-like part for high frequencies, separated by a time-varying cut-off frequency. In this study, we propose to model the time trajectories of the parameters of this HNM model for non-stationary signals, especially focusing on speech signals. This is done for time intervals up to several hundreds of milliseconds, thus significantly longer than usual short-term time frames used in analysis/synthesis models and in speech coders. The goal is to capture and exploit the long-term correlation of spectral components, as can appear across spectral parameters extracted from consecutive short-term frames. Previous works by Firouzmand et al. dealt with long-term parametric modelling in the more general framework of the sinusoidal model (i.e. long-term modelling of amplitude and phase parameters). We propose to extend this work to the HNM framework in order to obtain a complete long-term HNM model. In this latter case, the parameters to be modelled on the long-term basis are the spectral envelope (that encompasses the harmonic and noise regions), the fundamental frequency (which characterizes the harmonic region) and the cut-off frequency (which separates the harmonic and noise bands). To do this, the speech signal is first segmented into voiced (actually mixed voiced/unvoiced) sections and unvoiced sections, and a discrete cosine model is used for representing the time-trajectory of HNM parameters over each entire section. The proposed long-term HNM model can be used for music and speech analysis/synthesis. It enables joint compact representation of signals (thus a promising potential for low bit-rate coding) and easy signal manipulation directly from the long-term parameters (e.g. time stretching by direct interpolation). We present several experimentations to prove the efficiency of this model. For instance, the proposed long-term HNM is compared to the short-term version in terms of listening quality and data rate. Source

Farias R.C.,Grenoble Laboratory of Images | Brossier J.-M.,Grenoble Laboratory of Images
IEEE Transactions on Signal Processing | Year: 2014

In this paper, we study an asymptotic approximation of the Fisher information for the estimation of a scalar parameter using quantized measurements. We show that, as the number of quantization intervals tends to infinity, the loss of Fisher information induced by quantization decreases exponentially as a function of the number of quantization bits. A characterization of the optimal quantizer through its interval density and an analytical expression for the Fisher information are obtained. A comparison between optimal uniform and nonuniform quantization for the location and scale estimation problems shows that nonuniform quantization is only slightly better than uniform quantization. As the optimal quantization intervals are shown to depend on the unknown parameters, by applying adaptive algorithms that jointly estimate the parameter and set the thresholds in the location and scale estimation problems, we show that the asymptotic results can be approximately reached in practice using only 4 or 5 quantization bits. © 2014 IEEE. Source

Farias R.C.,Grenoble Laboratory of Images | Moisan E.,Grenoble Laboratory of Images | Brossier J.-M.,Grenoble Laboratory of Images
IEEE Signal Processing Letters | Year: 2014

Estimation of a location parameter based on noisy and binary quantized measurements is considered in this letter. We study the behavior of the Cramér-Rao bound as a function of the quantizer threshold for different symmetric unimodal noise distributions. We show that, in some cases, the intuitive choice of threshold position given by the symmetry of the problem, placing the threshold on the true parameter value, can lead to locally worst estimation performance. © 2014 IEEE. Source

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