Abdelhak M. Zoubir

The bootstrap and its application in signal processing

The bootstrap is an attractive tool for assessing the accuracy of estimators and testing hypothesis for parameters where conventional techniques are not valid, such as in small data-sample situations. We highlight the motivations for using the bootstrap in typical signal processing applications and give several practical examples. Bootstrap methods for testing statistical hypotheses are described and we provide an analysis of the accuracy of bootstrap tests. We also discuss how the bootstrap can be used to estimate a variance-stabilizing transformation to define a pivotal statistic, and we demonstrate the use of the bootstrap for constructing confidence intervals for flight parameters in a passive acoustic emission problem.

Signal processing techniques for landmine detection using impulse ground penetrating radar

Landmines are affecting the lives and livelihoods of millions of people around the world. A number of detection techniques, developed for use with impulse ground penetrating radar, are described, with emphasis on a Kalman filter based approach. Comparison of results from real data show that the Kalman filter algorithm provides the best detection performance, although its computational burden is also the highest.

Bootstrap Methods and Applications

Given the wealth of literature on the topic supported by solutions to practical problems, we would expect the bootstrap to be an off-the-shelf tool for signal processing problems as are maximum likelihood and least-squares methods. This is not the case, and we wonder why a signal processing practitioner would not resort to the bootstrap for inferential problems. We may attribute the situation to some confusion when the engineer attempts to discover the bootstrap paradigm in an overwhelming body of statistical literature. Our aim is to give a short tutorial of bootstrap methods supported by real-life applications. This pragmatic approach is to serve as a practical guide rather than a comprehensive treatment, which can be found elsewhere. However, for the bootstrap to be successful, we need to identify which resampling scheme is most appropriate.

Target Detection in Single- and Multiple-View Through-the-Wall Radar Imaging

A detector of targets behind walls and in enclosed structures is presented. The detector is applied to through-the-wall radar images obtained by wideband delay and sum beamforming. We consider the detection problem using single- and multiple-view imaging. The statistics of noise, clutter, and target images are examined and formulated using sample scenes. The effects of wall parameter errors on the image statistics are shown. An iterative detection scheme, which adapts itself to the image statistics, is presented. The proposed detection schemes are evaluated using real data.

Multipath exploitation in through-the-wall radar imaging using sparse reconstruction

Multipath exploitation and compressive sensing (CS) have both been applied independently to through-the-wall radar imaging (TWRI). Fast and efficient data acquisition is desired in scenarios where multipath effects cannot be neglected. Hence, we combine the two methods to achieve good image reconstruction in multipath environments from few spatial and frequency measurements. Ghost targets appear in the scene primarily due to specular reflections from interior walls and multiple reflections within the front wall. Assuming knowledge of the room geometry, we can invert the multipath model and eliminate ghosts by means of CS. We develop effective methods for the reconstruction of stationary scenes, which employ a group sparse CS approach. Additionally, we separate the target and wall contributions to the image by a sparse reconstruction approach joining wall and target models, which allows suppression of the ghosts and increased signal-to-clutter ratio (SCR) at the target locations. Effectiveness of the proposed approach is demonstrated using both simulated and real data.

Seizure detection of newborn EEG using a model-based approach

Seizures are often the first sign of neurological disease or dysfunction in the newborn. However, their clinical manifestation is often subtle, which tends to hinder their diagnosis at the earliest possible time. This represents an undesirable situation since the failure to quickly and accurately diagnose seizure can lead to longer-term brain injury or even death. Here, the authors consider the problem of automatic seizure detection in the neonate based on electroencephalogram (EEG) data. They propose a new approach based on a model for the generation of the EEG, which is derived from the histology and biophysics of a localized portion of the brain. They show that by using this approach, good detection performance of electrographic seizure is possible. The model for seizure is first presented along with an estimator for the model parameters. Then the authors present a seizure-detection scheme based on the model parameter estimates. This scheme is compared with the quadratic detection filter (QDF), and is shown to give superior performance over the latter. This is due to the ability of the model-based detector to account for the variability (nonstationarity) of the EEG by adjusting its parameters appropriately.

Detection of sources using bootstrap techniques

Source detection in array processing can be viewed as a test for equality of eigenvalues. Such a test is proposed, based on a multiple test procedure that considers all pairwise comparisons between eigenvalues. Using the bootstrap to estimate the null distributions of the test statistics results in a procedure with minimal assumptions on the nature of the signal. Simulations show that the proposed test is superior to information theoretic criteria such as the MDL, which are based on Gaussian signals and large sample sizes. Performance in most cases exceeds the more powerful sphericity test.

A method for estimating the parameters of the K distribution

A method that combines the maximum likelihood and the method of moments for estimating the parameters of the K distribution is proposed. The method results in the lowest variance of parameter estimates when compared with existing non-ML techniques.

Local polynomial Fourier transform: A review on recent developments and applications

The local polynomial Fourier transform (LPFT), as a high-order generalization of the short-time Fourier transform (STFT), has been developed and used for many different applications in recent years. This paper attempts to review previous research work on the following issues of the LPFT. Firstly, the definition, the properties of the LPFT and its relationships with other transforms are reviewed. The LPFT for multicomponent signal is then presented. The polynomial time frequency transform (PTFT), which is the maximum likelihood estimator to estimate the parameters in the LPFT, as well as its properties and fast algorithms are discussed. By comparing with the Fourier transform (FT), the STFT and the Wigner-Ville distribution (WVD), the LPFT has its superiority in obtaining improved SNRs, which can be supported by theoretical analysis and computer simulations. Furthermore, the reassignment method is combined with the LPFT and the robust LPFT to improve the concentration of the signal representation in the time-frequency domain. Performances obtained by using various LPP-related methods are compared for signals in different noise environments, such as the additive white Gaussian noise (AGWN), impulsive noise, and the mixture of AGWN and impulsive noise.

Analysis of Multicomponent Polynomial Phase Signals

While the theory of estimation of monocomponent polynomial phase signals is well established, the theoretical and methodical treatment of multicomponent polynomial phase signals (mc-PPSs) is limited. In this paper, we investigate several aspects of parameter estimation for mc-PPSs and derive the Crameacuter-Rao bound. We show the limits of existing techniques and then propose a nonlinear least squares (NLS) approach. We also motivate the use the Nelder-Mead simplex algorithm for minimizing the nonlinear cost function. The slight increase in computational complexity is a tradeoff for improved mean square error performance, which is evidenced by simulation results