Marie-Françoise Lucas

Compression of Biomedical Signals With Mother Wavelet Optimization and Best-Basis Wavelet Packet Selection

We propose a novel scheme for signal compression based on the discrete wavelet packet transform (DWPT) decompositon. The mother wavelet and the basis of wavelet packets were optimized and the wavelet coefficients were encoded with a modified version of the embedded zerotree algorithm. This signal dependant compression scheme was designed by a two-step process. The first (internal optimization) was the best basis selection that was performed for a given mother wavelet. For this purpose, three additive cost functions were applied and compared. The second (external optimization) was the selection of the mother wavelet based on the minimal distortion of the decoded signal given a fixed compression ratio. The mother wavelet was parameterized in the multiresolution analysis framework by the scaling filter, which is sufficient to define the entire decomposition in the orthogonal case. The method was tested on two sets of ten electromyographic (EMG) and ten electrocardiographic (ECG) signals that were compressed with compression ratios in the range of 50%-90%. For 90% compression ratio of EMG (ECG) signals, the percent residual difference after compression decreased from (mean ) 48.69.9% (21.58.4%) with discrete wavelet transform (DWT) using the wavelet leading to poorest performance to 28.43.0% (6.71.9%) with DWPT, with optimal basis selection and wavelet optimization. In conclusion, best basis selection and optimization of the mother wavelet through parameterization led to substantial improvement of performance in signal compression with respect to DWT and randon selection of the mother wavelet. The method provides an adaptive approach for optimal signal representation for compression and can thus be applied to any type of biomedical signal.

Optimization of wavelets for classification of movement-related cortical potentials generated by variation of force-related parameters

The paper presents a novel pattern recognition approach for the classification of single-trial movement-related cortical potentials (MRCPs) generated by variations of force-related parameters during voluntary tasks. The feature space was built from the coefficients of a discrete dyadic wavelet transformation. Mother wavelet parameterization allowed the tuning of basis functions to project the signals. The mother wavelet was optimized to minimize the classification error estimated from the training set. Classification was performed with a support vector machine (SVM) approach with optimization of the width of a Gaussian kernel and of the regularization parameter. The efficacy of the optimization procedures was representatively shown on electroencephalographic recordings from two subjects who performed unilateral isometric plantar flexions at two target torques and two rates of torque development. The proposed classification method was tested on four pairs of classes corresponding to the change in only one of the two parameters of the task. Misclassification rate (test set) in the classification of 1-s EEG activity immediately before the onset of the tasks was reduced from 50.8+/-2.9% with worst wavelet and nearest representative classifier, to 40.2+/-7.3% with optimal wavelet and nearest representative classifier, and to 15.8+/-3.4% with optimal wavelet and SVM with optimization of the kernel and regularization parameter. The proposed pattern recognition method is promising for classification of MRCPs modulated by variations of force-related parameters.

Optimal wavelets for biomedical signal compression.

Signal compression is gaining importance in biomedical engineering due to the potential applications in telemedicine. In this work, we propose a novel scheme of signal compression based on signal-dependent wavelets. To adapt the mother wavelet to the signal for the purpose of compression, it is necessary to define (1) a family of wavelets that depend on a set of parameters and (2) a quality criterion for wavelet selection (i.e., wavelet parameter optimization). We propose the use of an unconstrained parameterization of the wavelet for wavelet optimization. A natural performance criterion for compression is the minimization of the signal distortion rate given the desired compression rate. For coding the wavelet coefficients, we adopted the embedded zerotree wavelet coding algorithm, although any coding scheme may be used with the proposed wavelet optimization. As a representative example of application, the coding/encoding scheme was applied to surface electromyographic signals recorded from ten subjects. The distortion rate strongly depended on the mother wavelet (for example, for 50% compression rate, optimal wavelet, mean±SD, 5.46±1.01%; worst wavelet 12.76±2.73%). Thus, optimization significantly improved performance with respect to previous approaches based on classic wavelets. The algorithm can be applied to any signal type since the optimal wavelet is selected on a signal-by-signal basis. Examples of application to ECG and EEG signals are also reported.

Optimized Wavelets for Blind Separation of Nonstationary Surface Myoelectric Signals

Surface electromyography (EMG) signals detected over the skin surface may be mixtures of signals generated by many active muscles due to poor spatial selectivity of the recording. In this paper, we propose a new method for blind source separation (BSS) of nonstationary signals modeled as linear instantaneous mixtures. The method is based on whitening of the observations and rotation of the whitened observations. The rotation is performed by joint diagonalization of a set of spatial wavelet distributions (SWDs). The SWDs depend on the selection of the mother wavelet which can be defined by unconstrained parameters via the lattice parameterization within the multiresolution analysis framework. As the sources are classically supposed to be mutually uncorrelated, the design parameters of the mother wavelet can be blindly optimized by minimizing the average (over time lags) cross correlation between the estimated sources. The method was tested on simulated and experimental surface EMG signals and results were compared with those obtained with spatial time-frequency distributions and with second-order statistics (only spectral information). On a set of simulated signals, for 10-dB signal-to-noise ratio (SNR), the cross-correlation coefficient between original and estimated sources was 0.92plusmn0.07 with wavelet optimization, 0.74plusmn0.09 with the wavelet leading to the poorest performance, 0.85plusmn0.07 with Wigner-Ville distribution, 0.86plusmn0.07 with Choi-Williams distribution, and 0.73plusmn0.05 with second-order statistics. In experimental conditions, when the flexor carpi radialis and pronator teres were concomitantly active for 50% of the time, crosstalk was 55.2plusmn10.0% before BSS and was reduced to 15.2plusmn6.3% with wavelet optimization, 30.1plusmn15.0% with the worst wavelet, 28.3plusmn12.3% with Wigner-Ville distribution, 26.2plusmn12.0% with Choi-Williams distribution, and 35.1plusmn15.5% with second-order statistics. In conclusion, the proposed approach resulted in better performance than previous methods for the separation of nonstationary myoelectric signals.

Signal-dependent wavelets for electromyogram classification

In the study, an efficient method to perform supervised classification of surface electromyogram (EMG) signals is proposed. The method is based on the choice of a relevant representation space and its optimisation with respect to a training set. As EMG signals are the summation of compact-support waveforms (the motor unit action potentials), a natural tool for their representation is the discrete dyadic wavelet transform. The feature space was thus built from the marginals of a discrete wavelet decomposition. The mother wavelet was designed to minimise the probability of classification error estimated on the learning set (supervised classification). As a representative example, the method was applied to simulate surface EMG signals generated by motor units with different degrees of short-term synchronisation. The proposed approach was able to distinguish surface EMG signals with degrees of synchronisation that differed by 10%, with a misclassification rate of 8%. The performance of a spectral-based classification (error rate approximately 33%) and of the classification with Daubechies wavelet (21%) was significantly poorer than with the proposed wavelet optimisation. The method can be used for a number of different application fields of surface EMG classification, as the feature space is adapted to the characteristics of the signal that discriminate between classes.

A Novel Criterion of Wavelet Packet Best Basis Selection for Signal Classification With Application to Brain–Computer Interfaces

This study proposes a method to select a wavelet basis for classification. It uses a strategy defined by Wickerhauser and Coifman and proposes a new additive criterion describing the contrast between classes. Its performance is compared with other approaches on simulated signals and on experimental EEG signals for brain-computer interface applications.

Design of wavelets adapted to signals and application

This paper addresses the design of wavelets adapted to the processed signals and the considered application. Our approach consists of parameterizing a mother wavelet, and defining a quality criterion for the optimization of the parameters, according to the context. The first parameterization, leading to orthogonal wavelets, considers the coefficients of the scaling filter as the parameters. A second parameterization, leading to semiorthogonal wavelets, consists of convolving an existing wavelet (or scaling function) by a given sequence. In this paper, we explore these two methods and apply them to the supervised classification of signals made of waveform trains.

Wavelet optimization for classification

This paper addresses supervised signal classification using discrete time-scale representations. Given a set of learning signals and a class of discrete wavelet-basis, we propose to select the mother wavelet which yields the best classification results. This corresponds to determining the filter (used for the decomposition) that is ideally adapted to the specific classification problem at hand. It is realized by optimizing the filter coefficients according to a contrast criterion calculated on the learning set. Simulations show the efficiency of this approach.

Optimization of a set of wavelets for classification of imaginary movement-related cortical potentials

We have proposed an algorithm for optimization of a set of wavelets associated to multi-channel recordings. The method has been applied to the problem of classifying MRCPs in the context of BCIs. The preliminary results show that optimizing the wavelets may substantially improve the classification performance on a test set. These results must be confirmed in future studies on larger subject and signal samples.

Abrupt changes detection in the time-scale and in the time-frequency planes: a comparative study

We present in this paper a comparison between two segmentation approaches based on time-scale (t-s) and time-frequency (t-f) analysis. The purpose is to detect abrupt changes in the spectral characteristics of multicomponent nonstationary signals. After exposing the two procedures, we carry out different synthetic simulations in order to test and compare the performances of the methods for strictly and not strictly stepwise stationary signals. Finally, we apply the algorithms to musical signals which are not exactly piecewise stationary. This study demonstrates the potential segmentation capability of the proposed methods.