International Journal of Wavelets, Multiresolution and Information Processing

This paper reports a new signal classification tool, a modified wavelet network called Thresholding Wavelet Networks (TWN). The network is designed for the purposes of classifying signals. The philosophy of the technique is that often the difference between signals may not lie in the spectral or temporal region where the signal strength is high. Unlike other wavelet networks, this network does not concentrate necessarily on the high-energy region of the input signals. The network iteratively identifies the suitable wavelet coefficients (scale and translation) that best differentiate the different signals provided during training, irrespective of the ability of these coefficients to represent the signals. The network is not limited to the changes in temporal location of the signal identifiers. This paper also reports the testing of the network using simulated signals.

Polysomnographic (sleep) signals are recorded from patients exhibiting symptoms of a suspected sleep disorder such as Obstructive Sleep Apnoea (OSA). These non-stationary signals are characterised by having both quantitative information in the frequency domain and rich, dynamic data in the time domain. The collected data is subsequently analysed by skilled visual evaluation to determine whether arousals are present, an approach which is both time-consuming and subjective. This paper presents a wavelet-based methodology which seeks to alleviate some of the problems of the above method by providing: (a) an automated mechanism by which the appropriate stage of sleep for disorder observation may be extracted from the composite electroencephalograph (EEG) data set and (b) an ensuing technique to assist in the diagnosis of full arousal by correlation of wavelet-extracted information from a number of specific patient data sources (e.g. pulse oximetry, electromyogram [EMG] etc.).

This paper deals with an application of wavelets for feature extraction and classification of machine faults in a real-world machine data analysis environment. We have utilized informative wavelet algorithm to generate wavelets and subsequent coefficients that are used as feature variables for classification and diagnosis of machine faults. Informative wavelets are classes of functions generated from a given analyzing wavelet in a wavelet packet decomposition structure in which for the selection of best wavelets, concepts from information theory, i.e. mutual information and entropy are utilized. Training data are used to construct probability distributions required for the computation of the entropy and mutual information. In our data analysis, we have used machine data acquired from a single cylinder engine under a series of induced faults in a test environment. The objective of the experiment was to evaluate the performance of the informative wavelet algorithm for the accuracy of classification results using a real-world machine data and to examine to what extent the results were influenced by different analyzing wavelets chosen for data analysis. Accuracy of classification results as related to the correlation structure of the coefficients is also discussed in the paper.

This paper proposes a novel algorithm to clean up a large collection of historical handwritten documents kept in the National Archives of Singapore. Due to the seepage of ink over long period of storage, the front page of each document has been severely marred by the reverse side writing. Earlier attempts have been made to match both sides of a page to identify the offending strokes originating from the back so as to eliminate them with the aid of a wavelet transform. Perfect matching, however, is difficult due to document skews, differing resolutions, inadvertently missing out reverse side and warped pages during image capture. A new approach is now proposed to do away with double side mapping by using a directional wavelet transform that is able to distinguish the foreground and reverse side strokes much better than the conventional wavelet transform. Experiments have shown that the method indeed enhances the readability of each document significantly after the directional wavelet operation without the need for mapping with its reverse side.

This article describes a new method of the measure and analysis of the jitter phenomenon. Presented analysis is focused on the case of the telecommunication systems, but can be easily extended to other systems. This research is a continuation of the earlier work on the phase noise and jitter measurement systems. Method shown in this paper does not require generation of the reference clock in contrast to classic methods. It is rather based on the combination of the wavelet analysis and relational pattern recognition. This new approach to the jitter measurement problem gives very interesting results which are worth for further exploration. Authors give not only proposal but show measurement algorithm, which allows to estimate the jitter parameters by measure relation between the jitter wavelet base functions. In the background comparison of a classic and wavelet approaches to the jitter measurement problem is presented. In addition, such topics like the wavelet type, its order, as well as calibrating methods are also discussed.

Function approximation methods based on frames or other overcomplete dictionaries of approximating functions offer advantages over the orthogonal schemes due to the fact that the associated redundancy may lead to better de-noising and reconstruction power. Wavelet packets represent special wavelet frames; they combine overcompleteness with high time-frequency localization power through an optimal frequency-then-time segmentation. Compared to cosine packets, which enable optimal adaptation through time-then-frequency segmentation, wavelet packets show a different time-frequency resolution trade-off that might be useful for analyzing some kinds of non-stationary phenomena. We study the properties of covariance non-stationary stochastic processes whose realizations are observed at very high frequencies; the data are supplied by time series of a stock market return index. For these complex processes the effectiveness of wavelet and cosine packets is explored by implementing entropic optimization, greedy approximation techniques and dimension reduction methods.

It is well known that the sensitivity to translations and orientations is a major drawback in 2D discrete wavelet transform (DWT). In this paper, we have proposed an effective scheme for rotation invariant adaptive wavelet packet transform. During decomposition, the wavelet coefficients are obtained by applying a polar transform (PT) followed by a row-shift invariant wavelet packet decomposition (RSIWPD). In the first stage, the polar transform generates a row-shifted image and is adaptive to the image size to achieve complete and minimum sampling rate. In the second stage, the RSIWPD is applied to the row-shifted image to generate rotation invariant but over completed subbands of wavelet coefficients. In order to reduce the redundancy and computational complexity, we adaptively select some subbands to decompose and form a best basis representation with minimal information cost with respect to an appropriate information cost function. With this best basis representation, the original image can be reconstructed easily by applying a row-shift invariant wavelet packet reconstruction (RSIWPR) followed by an inverse polar transform (IPT). In the experiments, we study the application of this representation for texture classification and achieve 96.5% classification accuracy.