International Journal of Wavelets, Multiresolution and Information Processing

In the literature 2D (or bivariate) wavelets are usually constructed as a tensor product of 1D wavelets. Such wavelets are called separable. However, there are various applications, e.g. in image processing, for which non-separable 2D wavelets are prefered. In this paper, we investigate the class of compactly supported orthonormal 2D wavelets that was introduced by Belogay and Wang.² A characteristic feature of this class of wavelets is that the support of the corresponding filter comprises only two rows. We are concerned with the biorthogonal extension of this kind of wavelets. It turns out that the 2D wavelets in this class are intimately related to some underlying 1D wavelet. We explore this relation in detail, and we explain how the 2D wavelet transforms can be realized by means of a lifting scheme, thus allowing an efficient implementation. We also describe an easy way to construct wavelets with more rows and shorter columns.

The problem of automatic beat recognition in the ECG is tackled using continuous wavelet transform modulus maxima (CWTMM). Features within a variety of ECG signals can be shown to correspond to various morphologies in the CWTMM domain. This domain has an easy interpretation and offers a useful tool for the automatic characterization of the different components observed in the ECG in health and disease. As an application of this enhanced time-frequency analysis technique for ECG signals, an R-wave detector is developed and tested using patient signals recorded in the Coronary Care Unit of the Royal Infirmary of Edinburgh (attaining a sensitivity of 99.53% and a positive predictive value of 99.73%) and with the MIT/BIH database (attaining a sensitivity of 99.70% and a positive predictive value of 99.68%).

We examine Kingsbury's dual-tree complex wavelet transform in the frequency domain where it can be formulated for standard wavelet filters without special filter design. We prove that the dual-tree filter bank construction leads to wavelets with vanishing negative frequency parts, present numerical examples illustrating the improvement of translation and rotation invariance for various standard wavelet filters and apply the method to the classification of signals.

We present a technique for studying refinable functions which are compactly supported. Refinable functions satisfy dilation equations and this technique focuses on the implications of the dilation equation at the edges of the support of the refinable function. This method is fruitful, producing new results regarding existence, uniqueness, smoothness and rate of growth of refinable functions.

This paper presents a novel technique for classifying human hand gestures based on stationary wavelet transform (SWT) and classification based on geometrical based moments and compares the results with the classification based on Hu-moments and wavelet approximate images. The technique uses view-based approach for representation of hand actions, and uses a cumulative image-difference technique where the time between the sequences of images is implicitly captured in the representation of action resulting in Motion History Images (MHI). These MHIs are decomposed into wavelet sub-images using SWT. Translation and scaling invariant moments are then computed from the resulting high scale low pass residue of the wavelet sub-images. These geometrical moments are used as the global image descriptors and are fed to Artificial Neural Network (ANN) for classification. The recognition criterion is established using backpropagation based multilayer perceptron (MLP). The experiments show that such a system can classify human hand gestures with a classification accuracy of 97%.

This paper presents an implementation of a wavelet analysis toolbox and its integration within Excel. The toolbox includes the discrete wavelet transform, inverse wavelet transform, wavelet-based de-noising, and an associated plotting utility. The transforms and the de-noising algorithms were implemented in a DLL using C++ while the user interfaces were developed using Visual Basic for Applications (VBA) forms. A simple technique was used to automate the transfer of data, associated properties, and user selections from the worksheet to the DLL, and the computed values from the DLL back to the worksheet. We show how the grouping and presentation of computed wavelet coefficients allow for multiresolution analysis and further processing within Excel. We highlight the benefits behind implementing the basic wavelet analysis functions in Excel with reference to MATLAB.

Liver diseases are a common medical problem, especially amongst the population of developing countries. Magnetic Resonance Cholangio Pancreatography (MRCP) has become the popular non-invasive, non-ionizing examination for analysis of the hepatobiliary structure in the liver. Unfortunately, conventional 2D MRCP images can be difficult to analyze for biliary tree anomalies, especially with volume effect, artefacts and noise present in these images, whilst good 3D MRI systems are costly for less affluent nations. This paper proposes a scale-space multi-resolution approach to a segment-based implementation of the popular region growing algorithm, to identify the hierarchical structure of the biliary tree in conventional 2D MRCP images. Results obtained are promising in aiding automatic processing of these images to assist medical practitioners in analyzing the biliary tract more efficiently. Application of the algorithm may be extended for telemedicine.

This paper describes an efficient and adaptive method of threshold estimation for removing impulse noise from images, based on Double Density Wavelet Transform (DDWT). The performance of image de-noising algorithms using wavelet transforms can be improved significantly by fixing an optimum threshold value, based on the analysis of the statistical parameters of subband coefficients. In this proposed method, the choice of the threshold estimation is carried out by analyzing the statistical parameters of the wavelet subband coefficients like standard deviation, arithmetic mean and geometrical mean. Here the noisy image is first decomposed into many levels to obtain different frequency bands using DDWT. Then soft thresholding method is used to remove the noisy coefficients, by fixing the optimum threshold value by the proposed method. Experimental results on several test images by using the proposed method show that, the proposed method yields significantly superior image quality and better Peak Signal-to-Noise Ratio (PSNR). Some comparisons with the best available results will be given in order to illustrate the effectiveness of the proposed algorithm.