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A binary wavelet transform (BWT) has several distinct advantages over a real wavelet transform when applied to binary data. No quantisation distortion is introduced and the transform is completely invertible. Since all the operations involved are modulo-2 arithmetic, it is extremely fast. The outstanding qualities of the BWT make it suitable for binary image-processing applications. The BWT, originally designed for binary images, is extended to the lossless compression of grey-level images. An in-place implementation structure of the BWT is explored. Then, a simple embedded lossless BWT-based image-coding algorithm called progressive partitioning binary wavelet-tree coder (PPBWC) is proposed. The proposed algorithm is simple in concept and implementation, but achieves promising lossless compression efficiency as compared with the conventional bitplane scanning methods. Small alphabets in the arithmetic coding, non-causal adaptive context modelling and source division are the major factors that contribute to the gain of compression efficiency of the PPBWC. Experimental results show that the PPBWC outperforms most of other embedded coders in terms of coding efficiency.

Gene expression data generated by DNA microarray experiments have provided a vast resource for medical diagnosis and disease understanding. Most prior work in analyzing gene expression data, however, focuses on predictive performance but not so much on deriving human understandable knowledge. This paper presents a systematic approach for learning and extracting rule-based knowledge from gene expression data. A class of predictive self-organizing networks known as Adaptive Resonance Associative Map (ARAM) is used for modelling gene expression data, whose learned knowledge can be transformed into a set of symbolic IF-THEN rules for interpretation. For dimensionality reduction, we illustrate how the system can work with a variety of feature selection methods. Benchmark experiments conducted on two gene expression data sets from acute leukemia and colon tumor patients show that the proposed system consistently produces predictive performance comparable, if not superior, to all previously published results. More importantly, very simple rules can be discovered that have extremely high diagnostic power. The proposed methodology, consisting of dimensionality reduction, predictive modelling, and rule extraction, provides a promising approach to gene expression analysis and disease understanding.

Wavelet neural networks combine the functions of time-frequency localization from the wavelet transform and of self-studying from the neural network, which make them particularly suitable for the classification of complex patterns. In this paper, an efficient object recognition method using boundary representation and the wavelet neural network is proposed. The method employs a wavelet neural network (WNN) to characterize the singularities of the object curvature representation and to perform the object classification at the same time and in an automatic way. The local time-frequency attributes of the singularities on the object boundary are detected by making a preliminary wavelet analysis of the curvature representation. Then, the discriminative scale-translation features of the singularities are stored as the initial scale-translation parameters of the wavelet nodes in the WNN. These parameters are trained to their optimum status during the learning stage. With our approach, as opposed to matching features by convolving the signal with wavelet functions at a large number of scales, the computational burden is significantly reduced. Only a few convolutions are performed at the optimum scale-translation grids during the classification, which makes it suitable for real-time recognition tasks. Compared with the artificial-neural-network-based approaches preceded by wavelet filter banks with fixed scale-translation parameters, the support vector machine (SVM) using traditional Fourier descriptors and K-nearest-neighbor ( K-NN) classifier based on the state-of-the-art shape descriptors, our scheme demonstrates superior and stable discrimination performance under various noisy and affine conditions.

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