D. Pastor | Telecom Bretagne (original) (raw)

Papers by D. Pastor

Computational Statistics & Data Analysis, 2008

In many applications, observations result from the random presence or absence of random signals i... more In many applications, observations result from the random presence or absence of random signals in independent and additive white Gaussian noise. When the observations are independent and the probabilities of presence of the signals are upper-bounded by some value in [0,1), a theoretical result is established for the noise standard deviation. The latter is the only positive real number satisfying a specific convergence criterion when the number of observations and the minimum amplitude of the signals tend to infinity. This convergence involves neither the probability distributions nor the probabilities of presence of the signals. An estimate of the noise standard deviation is derived from this theoretical result. A binary hypothesis test based upon this estimate is also proposed. This test performs the detection of signals whose norms are lower-bounded by some known real value and whose probabilities of presence are less than or equal to one half. Neither the estimate nor the test requires prior knowledge of the probability distributions of the signals. Experimental results are given for the case of practical importance where the signals are independent two-dimensional random vectors modelling modulated sinusoidal carriers. These experimental results suggest that the asymptotic conditions of the limit theorem are not so constraining and can certainly be significantly relaxed in practice. Typical applications concern radar, sonar, speech processing but also proximity sensing and Electronic (Warfare) Support Measures.

IEEE Transactions on Signal Processing, 2010

This paper provides central limit theorems for the wavelet packet decomposition of stationary ban... more This paper provides central limit theorems for the wavelet packet decomposition of stationary bandlimited random processes. The asymptotic analysis is performed for the sequences of the wavelet packet coefficients returned at the nodes of any given path of the M-band wavelet packet decomposition tree. It is shown that if the input process is centred and strictly stationary, these sequences converge in distribution to white Gaussian processes when the resolution level increases, provided that the decomposition filters satisfy a suitable property of regularity. For any given path, the variance of the limit white Gaussian process directly relates to the value of the input process power spectral density at a specific frequency. Index Terms Wavelet transforms, Band-limited stochastic processes, Spectral analysis. I. INTRODUCTION This paper addresses the statistical properties of the M-Band Discrete Wavelet Packet Transform, hereafter abbreviated as M-DWPT. In [1], asymptotic analysis is given for the correlation structure and the distribution of the M-Band wavelet packet coefficients of stationary random processes. The limit autocorrelation functions and distributions are shown to be the same for every M-DWPT path. This seems to be a paradox because the M-DWPT paths are characterised by several sequences of wavelet filters. Two arbitrary sequences are different, and thus, do not have the same properties. In addition, the

Publication in the conference proceedings of EUSIPCO, Marrakech, Morocco, 2013

In many applications, d-dimensional observations result from the random presence or absence of ra... more In many applications, d-dimensional observations result from the random presence or absence of random signals in independent and additive white Gaussian noise. An estimate of the noise standard deviation can then be very useful to detect or to estimate these signals, especially when standard likelihood theory cannot apply because of too little prior knowledge about the signal probability distributions. Recent results and algorithms have then emphasized the interest of sparsity hypotheses to design robust estimators of the noise standard deviation when signals have unknown distributions. As a continuation, the present paper introduces a new robust estimator for signals with probabilities of presence less than or equal to one half. In contrast to the standard MAD estimator, it applies whatever the value of d. This algorithm is applied to image denoising by wavelet shrinkage as well as to non-cooperative detection of radiocommunications. In both cases, the estimator proposed in the present paper outperforms the standard solutions used in such applications and based on the MAD estimator. The Matlab code corresponding to the proposed estimator is available at http://perso.telecom-bretagne.eu/pastor.

IEEE Transactions on Aerospace and Electronic Systems, 2011

Based on recent results that link sparsity hypotheses and robust statistics, a new noise variance... more Based on recent results that link sparsity hypotheses and robust statistics, a new noise variance estimator for application to communication electronic support (CES) is derived in this contribution. Numerical simulations indicate that the proposed estimator clearly outperforms the median absolute deviation measure. They also highlight the benefits of this new estimator for constant false alarm rate (CFAR) detection and show that it can be implemented in systems with high spectral scanning rate. The

2012 11th International Conference on Information Science, Signal Processing and their Applications (ISSPA), 2012

In this paper we address the problem of large dimension decoding in MIMO systems. The complexity ... more In this paper we address the problem of large dimension decoding in MIMO systems. The complexity of the optimal maximum likelihood detection makes it unfeasible in practice when the number of antennas, the channel impulse response length or the source constellation size become too high. We consider a MIMO system with finite constellation and model it as a system with sparse signal sources. We formulate the decoding problem as an underdetermined sparse source recovering problem and apply the ℓ 1 -minimization to solve it. The resulting decoding scheme is applied to large MIMO systems and to frequency selective channel . We also review the computational cost of some ℓ 1 -minimization algorithms. Simulation results show significant improvement compared to other existing receivers.

2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2011

We address the problem of blind source separation in the underdetermined and instantaneous mixtur... more We address the problem of blind source separation in the underdetermined and instantaneous mixture case. The proposed method is based on an algorithm developed by Aissa-El-Bey and al.. This algorithm requires a good choice of the noise threshold and does not take into account the noise contribution in the inversion process. In order to overcome these drawbacks, this paper presents a robust underdetermined blind source separation approach. Robustness is achieved by estimating the noise standard deviation and using this estimate in the inversion process and the expression of the noise threshold. The good performance of the proposed method is shown by comparison with state-of-the-art methods.

Computational Statistics & Data Analysis, 2008

In many applications, observations result from the random presence or absence of random signals i... more In many applications, observations result from the random presence or absence of random signals in independent and additive white Gaussian noise. When the observations are independent and the probabilities of presence of the signals are upper-bounded by some value in [0,1), a theoretical result is established for the noise standard deviation. The latter is the only positive real number satisfying a specific convergence criterion when the number of observations and the minimum amplitude of the signals tend to infinity. This convergence involves neither the probability distributions nor the probabilities of presence of the signals. An estimate of the noise standard deviation is derived from this theoretical result. A binary hypothesis test based upon this estimate is also proposed. This test performs the detection of signals whose norms are lower-bounded by some known real value and whose probabilities of presence are less than or equal to one half. Neither the estimate nor the test requires prior knowledge of the probability distributions of the signals. Experimental results are given for the case of practical importance where the signals are independent two-dimensional random vectors modelling modulated sinusoidal carriers. These experimental results suggest that the asymptotic conditions of the limit theorem are not so constraining and can certainly be significantly relaxed in practice. Typical applications concern radar, sonar, speech processing but also proximity sensing and Electronic (Warfare) Support Measures.

IEEE Transactions on Signal Processing, 2010

This paper provides central limit theorems for the wavelet packet decomposition of stationary ban... more This paper provides central limit theorems for the wavelet packet decomposition of stationary bandlimited random processes. The asymptotic analysis is performed for the sequences of the wavelet packet coefficients returned at the nodes of any given path of the M-band wavelet packet decomposition tree. It is shown that if the input process is centred and strictly stationary, these sequences converge in distribution to white Gaussian processes when the resolution level increases, provided that the decomposition filters satisfy a suitable property of regularity. For any given path, the variance of the limit white Gaussian process directly relates to the value of the input process power spectral density at a specific frequency. Index Terms Wavelet transforms, Band-limited stochastic processes, Spectral analysis. I. INTRODUCTION This paper addresses the statistical properties of the M-Band Discrete Wavelet Packet Transform, hereafter abbreviated as M-DWPT. In [1], asymptotic analysis is given for the correlation structure and the distribution of the M-Band wavelet packet coefficients of stationary random processes. The limit autocorrelation functions and distributions are shown to be the same for every M-DWPT path. This seems to be a paradox because the M-DWPT paths are characterised by several sequences of wavelet filters. Two arbitrary sequences are different, and thus, do not have the same properties. In addition, the

Publication in the conference proceedings of EUSIPCO, Marrakech, Morocco, 2013

In many applications, d-dimensional observations result from the random presence or absence of ra... more In many applications, d-dimensional observations result from the random presence or absence of random signals in independent and additive white Gaussian noise. An estimate of the noise standard deviation can then be very useful to detect or to estimate these signals, especially when standard likelihood theory cannot apply because of too little prior knowledge about the signal probability distributions. Recent results and algorithms have then emphasized the interest of sparsity hypotheses to design robust estimators of the noise standard deviation when signals have unknown distributions. As a continuation, the present paper introduces a new robust estimator for signals with probabilities of presence less than or equal to one half. In contrast to the standard MAD estimator, it applies whatever the value of d. This algorithm is applied to image denoising by wavelet shrinkage as well as to non-cooperative detection of radiocommunications. In both cases, the estimator proposed in the present paper outperforms the standard solutions used in such applications and based on the MAD estimator. The Matlab code corresponding to the proposed estimator is available at http://perso.telecom-bretagne.eu/pastor.

IEEE Transactions on Aerospace and Electronic Systems, 2011

Based on recent results that link sparsity hypotheses and robust statistics, a new noise variance... more Based on recent results that link sparsity hypotheses and robust statistics, a new noise variance estimator for application to communication electronic support (CES) is derived in this contribution. Numerical simulations indicate that the proposed estimator clearly outperforms the median absolute deviation measure. They also highlight the benefits of this new estimator for constant false alarm rate (CFAR) detection and show that it can be implemented in systems with high spectral scanning rate. The

2012 11th International Conference on Information Science, Signal Processing and their Applications (ISSPA), 2012

In this paper we address the problem of large dimension decoding in MIMO systems. The complexity ... more In this paper we address the problem of large dimension decoding in MIMO systems. The complexity of the optimal maximum likelihood detection makes it unfeasible in practice when the number of antennas, the channel impulse response length or the source constellation size become too high. We consider a MIMO system with finite constellation and model it as a system with sparse signal sources. We formulate the decoding problem as an underdetermined sparse source recovering problem and apply the ℓ 1 -minimization to solve it. The resulting decoding scheme is applied to large MIMO systems and to frequency selective channel . We also review the computational cost of some ℓ 1 -minimization algorithms. Simulation results show significant improvement compared to other existing receivers.

2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2011

We address the problem of blind source separation in the underdetermined and instantaneous mixtur... more We address the problem of blind source separation in the underdetermined and instantaneous mixture case. The proposed method is based on an algorithm developed by Aissa-El-Bey and al.. This algorithm requires a good choice of the noise threshold and does not take into account the noise contribution in the inversion process. In order to overcome these drawbacks, this paper presents a robust underdetermined blind source separation approach. Robustness is achieved by estimating the noise standard deviation and using this estimate in the inversion process and the expression of the noise threshold. The good performance of the proposed method is shown by comparison with state-of-the-art methods.