Eric Grivel

Audio digital watermarking based on hybrid spread spectrum

Watermarking is a technique used to label digital media, to protect copyright ownership, by hiding information into the signal. Watermarks must be imperceptible and robust against attacks. Besides, watermark robustness against several signal processing techniques can be ensured by exploiting a technique related to spread spectrum communications. In this paper, we propose a procedure based on frequential substitution using a BPSK modulation with an adaptive carrier frequency, the choice of which depends on the original signal features. A secret key, generated during the watermarking process, is used for retrieving hidden information.

Subspace state space model identification for speech enhancement

This paper deals with Kalman filter-based enhancement of a speech signal contaminated by a white noise, using a single microphone system. Such a problem can be stated as a realization issue in the framework of identification. For such a purpose we propose to identify the state space model by using subspace non-iterative algorithms based on orthogonal projections. Unlike estimate-maximize (EM)-based algorithms, this approach provides, in a single iteration from noisy observations, the matrices related to state space model and the covariance matrices that are necessary to perform Kalman filtering. In addition no voice activity detector is required unlike existing methods. Both methods proposed here are compared with classical approaches.

Estimation of autoregressive fading channels based on two cross-coupled H∞ filters

This paper deals with the on-line estimation of time-varying frequency-flat Rayleigh fading channels based on training sequences and using H∞ filtering. When the fading channel is approximated by an autoregressive (AR) process, the AR model parameters must be estimated. As their direct estimations from the available noisy observations at the receiver may yield biased values, the joint estimation of both the channel and its AR parameters must be addressed. Among the existing solutions to this joint estimation issue, Expectation Maximization (EM) algorithm or cross-coupled filter based approaches can be considered. They usually require Kalman filtering which is optimal in the H2 sense provided that the initial state, the driving process and measurement noise are independent, white and Gaussian. However, in real cases, these assumptions may not be satisfied. In addition, the state-space matrices and the noise variances are not necessarily accurately estimated. To take into account the above problem, we propose to use two cross-coupled H∞ filters. This method makes it possible to provide robust estimation of the fading channel and its AR parameters.

Evaluating dissimilarities between two moving-average models: A comparative study between Jeffrey's divergence and Rao distance

The autoregressive models (AR) and moving-average models (MA) are regularly used in signal processing. Previous works have been done on dissimilarity measures between AR models by using a Riemannian distance, the Jeffreys divergence (JD) and the spectral distances such as the Itakura-Saito divergence. In this paper, we compare the Rao distance and the JD for MA models and more particularly in the case of 1st-order MA models for which an analytical expression of the inverse of the covariance matrix is available. More particularly, we analyze the advantages of the Rao distance use. Secondly, the simulation part compares both dissimilarity measures depending on the MA parameters but also on the number of data available.

Noisy speech dereverberation as a SIMO system identification issue

This paper deals with the speech dereverberation issue based on a single input multiple output (SIMO) system, when the reverberations are modeled by finite impulse response (FIR) filters. In most of the existing methods, the authors assume either that the white noises have the same variance or that the noise statistics are available. Here, we investigate the blind speech deconvolution using two microphones, when the white noise variances are not equal. For this purpose, we present a modified version of an identification approach previously developed in the framework of control and based on the properties of the definiteness and the positiveness of the autocorrelation matrices of the reverberated versions of the speech and the observations. This makes it possible to estimate both the variances of the additive noises and the FIR. Then, the speech signal is retrieved in the least square (LS) or minimum variance (MV) sense

Interpreting the asymptotic increment of Jeffrey's divergence between some random processes

Abstract In signal and image processing, Jeffreys divergence (JD) is used in many applications for classification, change detection, etc. The previous studies done on the JD between ergodic wide-sense stationary (WSS) autoregressive (AR) and/or moving average (MA) processes state that the asymptotic JD increment, which is the difference between two JDs based on k and ( k − 1 ) -dimensional random vectors when k becomes high, tends to a constant value, except JDs which involve a 1st-order MA process whose power spectral density (PSD) is null for one frequency. In this paper, our contribution is threefold. We first propose an interpretation of the asymptotic JD increment for ergodic WSS ARMA processes: it consists in calculating the power of the first process filtered by the inverse filter associated with the second process and conversely. This explains the atypical cases identified in previous works and generalizes them to any ergodic WSS ARMA process of any order whose PSD is null for one or more frequencies. Then, we suggest comparing other random processes such as noisy sums of complex exponentials (NSCE) by using the JD. In this case, the asymptotic JD increment and the convergence speed towards the asymptotic JD are useful to compare the processes. Finally, NSCE and pth-order AR processes are compared. The parameters of the processes, especially the powers of the processes, have a strong influence on the asymptotic JD increment.

Jeffrey's divergence between autoregressive moving-average processes

Various works have been carried out about the Jeffreys divergence (JD) which is the symmetric version of the Kullback-Leibler (KL) divergence. An expression of the JD for Gaussian processes can be deduced from the definition of the KL divergence and the expression of the Gaussian-multivariate distributions of k-dimensional random vectors. It depends on the k × k Toeplitz covariance matrices of the stationary processes. However, the resulting computational cost may be high as these matrices must be inverted and it is all the higher as k increases. To circumvent this problem, a recursive expression can be obtained for real 1st-order autoregressive (AR) processes. When they are disturbed by additive uncorrelated white noises, we showed that when k becomes large, the derivative of the JD with respect to k tends to be constant. This constant is sufficient to compare the noisy AR processes. In this paper, we propose to extend our work to AR moving-average (MA) processes with one AR term and one MA term. Some examples illustrate the theoretical analysis.

Comparing a complex-valued sinusoidal process with an autoregressive process using Jeffrey's divergence

This paper deals with the analysis of the Jeffreys divergence (JD) between an autoregressive process (AR) and a sum of complex exponentials (SCE), whose magnitudes are Gaussian random values, which is then disturbed by an additive white noise. As interpreting the value of the JD may not be necessarily an easy task, we propose to give an expression of the JD and to analyze the influence of each process parameter on it. More particularly, we show that the ratios between the variance of the additive white noise and the variance of the AR-process driving process on the one hand, and the sum of the ratios between the SCE process power and the AR-process PSD at the normalized angular frequencies on the other hand, has a strong impact on the JD. The 2-norm of the AR-parameter has also an influence. Illustrations confirm the theoretical part.

Process Comparison Combining Signal Power Ratio and Jeffrey’s Divergence Between Unit-Power Signals

Jeffrey’s divergence (JD), the symmetric Kullback-Leibler (KL) divergence, has been used in a wide range of applications. In recent works, it was shown that the JD between probability density functions of k successive samples of autoregressive (AR) and/or moving average (MA) processes can tend to a stationary regime when the number k of variates increases. The asymptotic JD increment, which is the difference between two JDs computed for k and \(k-1\) successive variates tending to a finite constant value when k increases, can hence be useful to compare the random processes. However, interpreting the value of the asymptotic JD increment is not an easy task as it depends on too many parameters, i.e. the AR/MA parameters and the driving-process variances. In this paper, we propose to compute the asymptotic JD increment between the processes that have been normalized so that their powers are equal to 1. Analyzing the resulting JD on the one hand and the ratio between the original signal powers on the other hand makes the interpretation easier. Examples are provided to illustrate the relevance of this way to operate with the JD.

Jeffrey's Divergence Between ARFIMA Processes

Abstract The symmetric Kullback–Leibler divergence known as Jeffreys divergence (JD) has found applications in signal and image processing, from radar clutter modeling to texture analysis. Recently, several studies were done on the JD between ergodic wide-sense stationary autoregressive (AR) and/or moving average (MA) processes. It was shown that the so-called asymptotic JD increment can be useful to compare ergodic wide-sense stationary ARMA processes. An interpretation of the asymptotic JD increment was also proposed. It consists in calculating the power of the first process filtered by the inverse filter associated with the second process, and conversely. However, in some biomedical applications, econometrics and other areas, long-memory processes have rather to be studied. Therefore, this paper aims at addressing the JD between ergodic wide-sense stationary autoregressive fractionally integrated moving average (ARFIMA) processes. More particularly, we study the influence of the ARFIMA parameters on the value of the asymptotic JD increment. Then, we analyze if the interpretation of the asymptotic JD increment based on inverse filtering is still valid for this type of process. Finally, some simulation results illustrate the theoretical analysis.