International Journal of Wavelets, Multiresolution and Information Processing

This paper presents a novel technique for classifying human hand gestures based on stationary wavelet transform (SWT) and compares the results with classification based on Hu moments. The technique uses view-based approach for representation of hand actions, and artificial neural networks (ANN) for classification. This approach uses a cumulative image-difference technique where the time between the sequences of images is implicitly captured in the representation of action. This results in the construction of Motion History Images (MHI). These MHI's are decomposed into four sub-images using SWT. The average image (f_ll) is fed as the global image descriptors to the ANN for classification. The recognition criterion is established using backpropagation based multilayer perceptron (MLP). The preliminary experiments show that such a system can classify human hand gestures with a classification accuracy of 97%. The work is motivated by the previous research in appearance-based motion recognition of human hand actions. The overall goal of our research is to determine the reliability of using this wavelet based computationally inexpensive gesture classification technique that may be used for helping disabled or aged people interact with computers.

This paper presents a fusion scheme for wavelets and fractal image compression based on the self-similarity of the space-frequency plane of sub-bands after wavelet transformation of images. Various kinds of wavelet transform are examined for the characteristics of their self-similarity and evaluated for the adoption of fractal encoder. The aim of this paper is to reduce the information of the two sets of blocks involved in the fractal image compression by using the self-similarity of images. And also, the new video encoder using the fusion method of wavelets and fractal adopts the similar manner as the motion compensation technique of MPEG encoder. Experimental results show almost the same PSNR and bits rate as conventional fractal image encoder by depending on the sampled images through computer simulations.

This paper presents a wavelet transform (WT) based on simultaneous de-noising and compression scheme for noisy signal. Due to the downsampling in decomposition process, the orthogonal wavelet transform (OWT) is translation variant, which significantly hinders its performance in coding and denoising. In this paper the wavelet bintree decomposition (WBD), which is equivalent to a translation invariant WT, is first formed and an optimal downsampling route is then traversed among all the routes of the bintree. The WT with the optimal route would most effectively decorrelate and compactly represent the signal. During the process of noisy signal encoding, wavelet thresholding based denoising is performed. Thresholding is similar to the quantization of a zero-zone in lossy encoding procedure. We applied a signal-adaptive threshold to the wavelet coefficients and quantized the coefficients outside the zero-zone. Experiments show that the proposed scheme significantly outperforms the OWT-based method.

The wavelet transform seems particularly suited to analyse the electromyographic signal (EMG) during gait of asymptomatic and pathological subjects. Firstly, because physiologically the electrical activity generated by the muscles derives from a weighted sum of individual physiological components having limited support in time and in frequency. Secondly, because it is important to analyze muscle activity during specific phases of the cycle, and finally, because specific ranges of frequency are important pathological discriminators. In this paper we report the preliminary results of a project aimed at classifying asymptomatic and pathological subjects by analysing the complex wavelet transform of the EMG signal derived from two muscles (Tibialis Anterior and Lateral Gastrocnemius) during gait. An asymptomatic adult, an asymptomatic child and two pathological (cerebral palsy) children were examined using telemetric EMG devices and pressure footswitches. The results showed that the indices derived from the coefficient amplitudes (Gastrocnemius) and from frequency distribution (Tibialis) are capable of classifying the subjects into three groups. Despite the small number of cases analyzed, we believe that the relevance of the results deserves particular attention because of the novelty of the use of the wavelet transform for this application and of the potential application to monitor patients during interventions aimed at improving muscle behavior, particularly antispasticity treatment such as Botulinum Toxin injections.

In this paper we propose a simple forecasting strategy which exploits the multiresolution property of the wavelet transform. US aggregate retail sales data have strong trend and seasonal patterns, providing a good testing ground for the proposed forecasting method. First a wavelet transform is used to decompose the time series into varying scales of resolution so that the underlying temporal structures of the original time series become more tractable; the decomposition is additive in details and approximation. Then a forecasting engine (neural network or fuzzy inference system) is trained on each of the relevant resolution scales, and individual wavelet scale forecasts are recombined to form the overall forecast. Substantial information in both the dynamic nonlinear trend and seasonal patterns of the time series is efficiently exploited: we choose short past windows for the inputs to the forecasting engines at lower scales and long past windows at higher scales. The forecasting engines learn the mapping hierarchically: using a scale-recursive strategy, we combine only those scales where significant events are detected. Univariate simulation results on US aggregate retailing indicate that the proposed method fares favourably in relation to forecasting results obtained by training a neural network on original time series. Multivariate simulation results obtained by including structural components inflation, recession, interest rates, unemployment, show improvement in sales-trend forecast.

This paper introduces some properties of symmetric Laurent polynomials, and then extends Euclidean algorithm to symmetric Laurent polynomials. The new results are used to investigate factorization of polyphase matrix for biorthogonal finite filters. It is shown that there exists one and only one symmetric factorization of the polyphase matrix, and the symmetric factorization can be determined directly and efficiently by Euclidean algorithm for symmetric Laurent polynomials. Finally, symmetric implementation and matrix representation of biorthogonal wavelet transforms are introduced, and the study demonstrates that the symmetric implementation has the least multiplication number in all lifting implementations, and it is equivalent to a matrix transform on finite dimensional vector space.

We prove a theorem to characterize the p-frames for a shift invariant closed subspace of Wiener amalgam spaces , 1 ≤ p ≤ q ≤ ∞, being a locally compact abelian group. Also, we show that a collection of translates under approximate conditions generaltes a p-frames for the space .