Meryem Jabloun

Estimation of the instantaneous amplitude and frequency of non-stationary short-time signals

We consider the modeling of non-stationary discrete signals whose amplitude and frequency are assumed to be nonlinearly modulated over very short-time duration. We investigate the case where both instantaneous amplitude (IA) and instantaneous frequency (IF) can be approximated by orthonormal polynomials. Previous works dealing with polynomial approximations refer to orthonormal bases built from a discretization of continuous-time orthonormal polynomials. As this leads to a loss of the orthonormal property, we propose to use discrete orthonormal polynomial bases: the discrete orthonormal Legendre polynomials and a discrete base we have derived using Gram-Schmidt procedure. We show that in the context of short-time signals the use of these discrete bases leads to a significant improvement in the estimation accuracy. We manage the model parameter estimation by applying two approaches. The first is maximization of the likelihood function. This function being highly nonlinear, we propose to apply a stochastic optimization technique based on the simulated annealing algorithm. The problem can also be considered as a Bayesian estimation which leads us to apply another stochastic technique based on Monte Carlo Markov Chains. We propose to use a Metropolis Hastings (MH) algorithm. Both approaches need an algorithm parameter tuning that we discuss according our application context. Monte Carlo simulations show that the results obtained are close to the Cramer-Rao bounds we have derived. We show that the first approach is less biased than the second one. We also compared our results with the higher ambiguity function-based method. The methods proposed outperform this method at low signal to noise ratios (SNR) in terms of estimation accuracy and robustness. Both proposed approaches are of a great utility when scenarios in which signals having a small sample size are non-stationary at low SNRs. They provide accurate system descriptions which are achieved with only a reduced number of basis functions.

A New Flexible Approach to Estimate the IA and IF of Nonstationary Signals of Long-Time Duration

In this paper, we propose an original strategy for estimating and reconstructing monocomponent signals having a high nonstationarity and long-time duration. We locally apply to short-time duration intervals the strategy developed in our previous work about nonstationary short-time signals. This paper describes a nonsequential time segmentation that provides segments whose lengths are suitable for modeling both the instantaneous amplitude and frequency locally with low-order polynomials. Parameter estimation is done independently for each segment by maximizing the likelihood function by means of the simulated annealing technique. The signal is then reconstructed by merging the estimated segments. The strategy proposed is sufficiently flexible for estimating a large variety of nonstationarity and specifically applicable to high-order polynomial phase signals. The estimation of a high-order model is not necessary. The error propagation phenomenon occurring with the known approach, the higher ambiguity function (HAF)-based method, is avoided. The proposed strategy is evaluated using Monte Carlo noise simulations and compared with the Cramer-Rao bounds (CRBs). The signal of a songbird is used as a real example of its applicability.

A AM/FM single component signal reconstruction using a nonsequential time segmentation and polynomial modeling

Summary form only given. The problem of estimating nonstationary signals has been considered in many previous publications. In this paper we propose an alternative algorithm in order to accurately estimate AM/FM signals. Only single component signals are considered. We perform local polynomial modeling on short time segments using a nonsequential strategy. The degree of polynomial approximation is limited due to the shortness of each time segment. The time support of a segment is controlled by a criterion defined on the spectrogram. To keep optimality a maximum likelihood procedure estimates the local model parameters leading to a nonlinear equation system in R7. This is solved by a simulated annealing technique. Finally, the local polynomial models are merged to reconstruct the entire signal model. The proposed algorithm enables highly nonlinear AM/FM estimation and shows robustness even when signal to noise ratio (SNR) is low. The appropriate Cramer Rao bounds (CRB) are presented for both polynomial phase and amplitude signals. Monte Carlo simulations show that the proposed algorithm performs well. Finally, our proposed method is illustrated using both numerical simulations and a real signal of whale sound.

Maximum likelihood parameter estimation of short-time multicomponent signals with nonlinear AM/FM modulation

Parameter estimation for closely spaced or crossing frequency trajectories is a difficult signal processing problem, especially in the presence of both nonlinear amplitude and frequency modulations. In this paper, polynomial models are assumed for the instantaneous frequencies and amplitudes (IF/IA). We suggest two different strategies to process multicomponent signals. In the first one, which is optimal, all model parameters are simultaneously estimated using a maximum likelihood procedure (ML), maximized via a stochastic technique called simulated annealing (SA). In the second strategy, which is suboptimal, the signal is iteratively reconstructed component by component. At each iteration, the IF and IA of one component are estimated using the ML procedure and the SA technique. To evaluate the accuracy of the proposed strategies, Monte Carlo simulations are presented and compared to the derived Cramer-Rao bounds for closely spaced and crossing frequency trajectories. The results show the proposed algorithms perform well compared to existing techniques

A generating model of realistic synthetic heart sounds for performance assessment of phonocardiogram processing algorithms

Abstract A new model which is capable of generating realistic synthetic phonocardiogram (PCG) signals is introduced based on three coupled ordinary differential equations. The new PCG model takes into account the respiratory frequency, the heart rate variability and the time splitting of first and second heart sounds. This time splitting occurs with each cardiac cycle and varies with inhalation and exhalation. Clinical PCG statistics and the close temporal relationship between events in ECG and PCG are used to deduce values of PCG model parameters. In comparison with published PCG models, the proposed model allows a larger number of known PCG features to be taken into consideration. Moreover it is able to generate both normal and abnormal realistic synthetic heart sounds. Results show that these synthetic PCG signals have the closest features to those of a conventional heart sound in both time and frequency domains. Additionally, a sound quality test carried out by eight cardiologists demonstrates that the proposed model outperforms the existing models. This new PCG model is promising and useful in assessing signal processing techniques which are developed to help clinical diagnosis based on PCG.

Assessment of an MCMC algorithm convergence for Bayesian estimation of the particle size distribution from multiangle dynamic light scattering measurements

Recovering the particle size distribution (PSD) from dynamic light scattering (DLS) measurements is known to be a highly ill-posed inverse problem. In a former study, we proposed a new Bayesian inference method applied directly to the multiangle DLS measurements to improve the estimation of multimodal PSDs. The posterior probability density of interest is sampled using a MCMC Metropolis-within-Gibbs algorithm. In this work, we experimentally examined the convergence of the used MCMC strategy using the simulation method recently proposed by Chauveau and Vandekerkhove (2013). This method is based on the evolution in time (iterations) of the Kullback-Leibler divergence between the target posterior density and the successive densities of the algorithm of interest. The convergence of the used MCMC algorithm was examined when processing simulated and experimental data.