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In this paper, a novel learning algorithm of wavelet networks based on the Fast Wavelet Transform (FWT) is proposed. It has many advantages compared to other algorithms, in which we solve the problem in previous works, when the weights of the hidden layer to the output layer are determined by applying the back propagation algorithm or by direct solution which requires to compute the matrix inversion, this may cause intensive computation when the learning data is too large. However, the new algorithm is realized by iterative application of FWT to compute the connection weights. Furthermore, we have extended the novel learning algorithm by using Levenberg–Marquardt method to optimize the learning functions. The experimental results have demonstrated that our model is remarkably more refreshing than some of the previously established models in terms of both speed and efficiency.

Taking advantage of both the scaling property of wavelets and the high learning ability of neural networks, wavelet networks have recently emerged as a powerful tool in many applications in the field of signal processing such as data compression, function approximation as well as image recognition and classification. A novel wavelet network-based method for image classification is presented in this paper. The method combines the Orthogonal Least Squares algorithm (OLS) with the Pyramidal Beta Wavelet Network architecture (PBWN). First, the structure of the Pyramidal Beta Wavelet Network is proposed and the OLS method is used to design it by presetting the widths of the hidden units in PBWN. Then, to enhance the performance of the obtained PBWN, a novel learning algorithm based on orthogonal least squares and frames theory is proposed, in which we use OLS to select the hidden nodes. In the simulation part, the proposed method is employed to classify colour images. Comparisons with some typical wavelet networks are presented and discussed. Simulations also show that the PBWN-orthogonal least squares (PBWN-OLS) algorithm, which combines PBWN with the OLS algorithm, results in better performance for colour image classification.

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This paper presents a new approach of face recognition based on wavelet network using 2D fast wavelet transform and multiresolution analysis. This approach is divided in two stages: the training stage and the recognition stage. The first consists to approximate every training face image by a wavelet network. The second consists in recognition of a new test image by comparing it to all the training faces, the distances between this test face and all images from the training set are calculated in order to identify the searched person. The usual training algorithms presents some disadvantages when the weights of the wavelet network are computed by applying the back-propagation algorithm or by direct solution which requires computing an inversion of matrix, this computation may be intensive when the learning data is too large. We present in this paper our solutions to overcome these limitations. We propose a novel learning algorithm based on the 2D Fast Wavelet Transform. Furthermore, we have increased the performances of our algorithm by introducing the Levenberg–Marquardt method to optimize the learning functions and using the Beta wavelet which has at both an analytical expression and wavelet filter bank. Extensive empirical experiments are performed to compare the proposed method with other approaches as PCA, LDA, EBGM and RBF neural network using the ORL and FERET benchmarks.