Abdeldjalil Ouahabi

Analytical formulation of the fractal dimension of filtered stochastic signals

The aim of this study was to investigate the effects of a linear filter on the regularity of a given stochastic process in terms of the fractal dimension. This general approach, described in a continuous time domain, is new and is characterized by its simplicity. The framework of this problem is general since it emerges when a fractal process undertakes a transformation, as is the case in denoising or measurement processes.

Spectrum estimation from randomly sampled velocity data [LDV]

The power spectral density of randomly sampled signals is studied with reference to fluid velocity measured by laser Doppler velocimetry. We propose a new method for spectral estimation of Poisson-sampled stochastic processes. Our approach is based on polygonal interpolation from the sampled process followed by resampling and the usual fast Fourier transform. This study emphasizes the merit of the polygonal hold versus the sample-and-hold (zero order) and shows that polygonal interpolation results in better accuracy, especially at high frequencies. For purposes of illustrations the sampled process is assumed to be either a Kolmogorov or a Von Karman process. Numerical simulations and experimental results are given and confirm our theoretical analysis.

Perception and characterization of materials using signal processing techniques

In this paper, we develop a methodology and a conceptual framework in which manipulations are undertaken for perceiving and characterizing materials. Within this framework, we distinguish different materials (unknown environments) by actively contacting and testing them, and by analyzing the resulting sounds using a microphone. For this implementation, we identify sensor-derived measures that are diagnostic of a materials properties, and use these measures to categorize the objects (or unknown environments) in their different material class. The parameter of characterization is the internal angle of friction of the materials. This parameter is determined by the relation of strain and stress properties. Using this theoretical approach and the experimental results, we conclude that the statement of shape-invariance of materials is critical and invalid in real cases.

Estimation of the blood Doppler frequency shift by a time-varying parametric approach

Doppler ultrasound is widely used in medical applications to extract the blood Doppler flow velocity in the arteries via spectral analysis. The spectral analysis of non-stationary signals and particularly Doppler signals requires adequate tools that should present both good time and frequency resolutions. It is well-known that the most commonly used time-windowed Fourier transform, which provides a time-frequency representation, is limited by the intrinsic trade-off between time and frequency resolutions. Parametric methods have then been introduced as an alternative to overcome this resolution problem. However, the performance of those methods deteriorates when high non-stationarities are present in the Doppler signal. For the purpose of accurately estimating the Doppler frequency shift, even when the temporal flow velocity is rapid (high non-stationarity), we propose to combine the use of the time-varying autoregressive (AR) method and the (dominant) pole frequency. This proposed method performs well in the context where non-stationarities are very high. A comparative evaluation has been made between classical (FFT based) and AR (both block and recursive) algorithms. Among recursive algorithms we test an adaptive recursive method as well as a time-varying recursive method. Finally, the superiority of the time-varying parametric approach in terms of frequency tracking and delay in the frequency estimate is illustrated for both simulated and in vivo Doppler signals.

Harmonic propagation of finite amplitude sound beams: experimental determination of the nonlinearity parameter B/A

We propose a method to determine the nonlinearity parameter B/A of a liquid from the spatial evolution of harmonic components. We describe an analytical model, in the parabolic and quasi-linear approximations, that predicts the continuous finite amplitude sound beam propagation radiated by a plane piston source. This model takes into consideration attenuation, diffraction and nonlinear effects. The fundamental and second harmonic ultrasonic fields are expressed as the superposition of Gaussian beams. Axial propagation curves are then compared with those obtained by direct numerical solution of the transformed beam equation using the finite difference method, and with experimental results. Accurate measurements of pressure levels for the nonlinearly generated harmonics in water are performed along and across the propagation axis for different pressure values delivered at the piston surface. Experimental results, for water and ethanol, are in agreement with those of our model, which allows us to obtain the expected value of the nonlinearity parameter B/A.

Multifractal analysis for texture characterization: A new approach based on DWT

Texture characterization, which measures the fluctuations of image amplitude regularity in space, now often uses fractal and multifractal analysis. The present contribution deals with a multifractal approach in ultrasound skin images to characterize melanoma. In this paper, we propose to build new hierarchical multiresolutions quantities: Maximum coefficients of the Discrete Wavelet Transform for 2D Multifractal analysis. The performance of the proposed texture descriptors was evaluated for 2D synthetic processes and biomedical texture classification.

Delta high order cumulant-based recursive instrumental variable algorithm

This letter presents a new recursive high order cumulant-based instrumental variable algorithm. It is based on a modification of the classical least squares estimation and the utilization of the delta operator. The algorithm provides an expression of autoregressive (AR) parameters estimation, in which an additional term appears. This results in an improvement of the convergence of the classical q operator algorithm. Computer simulation results are given to illustrate the behavior of this method.

Random sampling: spectrum of fluid measured by Doppler velocimetry

Spectral analysis of randomly sampled signals is discussed with reference to fluid velocity measured by ultrasonic (or laser) Doppler velocimetry. This study summarizes the merits, in the mean square sense, of the polygonal hold vs the zero-order hold interpolator. The comparison is done for different sampling schemes, such as Poisson sampling. It can be shown that if the signal is sampled randomly with a Poisson method, the output signal is equal to the original signal plus an uncorrelated additive white noise. Our purpose is to reduce the effect of this noise by using a simple first-order (or polygonal) interpolator. Similar results can be derived for uniform sampling with some missing samples or with time jitter. Finally, we use a suboptimal method for detection of sampling jitter based on the bispectrum of sampled data.

Non-Stationary Parametric Spectral Estimation for Ultrasound Attenuation

Great progress1 has been made recently in high frequency ultrasound imaging. In particular, several works have shown the interest of echographic exploration for frequencies ranging from 20 to 100 MHz, in dermatology and ophthalmology. These results are extending the field cf application of tissue characterization. The measurement of acoustic attenuation tissues has received much interest in the field of ultrasound tissue characterization. Indeed, several clinical applications have shown a correlation between attenuation values and pathological states.

Wavelet-Based Multifractal Identification of Fracture Stages

Because fracture phenomena are highly nonlinear and non-stationary, the classical analyzis of fracture lines development is not adapted for their characterization. Multifractal analysis is now increasingly used to characterize these irregular patterns. In this investigation, multifractal analyzis based on the continuous Wavelet Transform Modulus Maxima method (WTMM) is proposed to give a multifractal discrimination of the profile lines development at different fracture stages: fracture initiation, fracture propagation and final rupture. This multifractal analyzis makes it possible to take into account the local regularity of fracture profiles. The degree of these fluctuations is quantified by Holder exponent α, computed from WTMM coefficients of the signal. The proposed wavelet-based multifractal approach is mainly compared to standard multifractal one based on the box-counting method (BCM). We noted that WTMM describes reasonably well the scaling properties of fracture patterns distributions at three distinct fracture stages. The results suggest that parameters of the multifractal spectrum such as the capacity dimension D0, the average singularity strength α0, the aperture of the left side α0−αq and the total width (αmax−αmin) of the f(α) spectra may be useful as parameters characterizing the different fracture stages and mechanisms of elastomeric material.