International Journal of Wavelets, Multiresolution and Information Processing

We present an algorithm that compresses two-dimensional data, which are piece-wise smooth in one direction and have oscillatory events in the other direction. Fine texture, seismic, hyper-spectral and fingerprints have this mixed structure. The transform part of the compression process is an algorithm that combines the application of the wavelet transform in one direction with the local cosine transform (LCT) in the other direction. This is why it is called hybrid compression. The quantization and the entropy coding parts in the compression process were taken from SPIHT codec but it can also be taken from any multiresolution based codec such as EZW. To efficiently apply the SPIHT codec to a mixed coefficients array, reordering of the LCT coefficients takes place. When oscillating events are present in different directions as in fingerprints or when the image comprises of a fine texture, a 2D LCT with coefficients reordering is applied. These algorithms outperform algorithms that are solely based on the the application of 2D wavelet transforms to each direction with either SPIHT or EZW coding including JPEG2000 compression standard. The proposed algorithms retain fine oscillating events including texture even at a low bitrate. Its compression capabilities are also demonstrated on multimedia images that have a fine texture. The wavelet part in the mixed transform of the hybrid algorithm utilizes the Butterworth wavelet transforms library that outperforms the 9/7 biorthogonal wavelet transform.

Over the past decade, there have been dramatic increases in the usage of mobile phones in the world. Currently available smart mobile phones are capable of storing enormous amounts of personal information/data. The smart mobile phone is also capable of connecting to other devices, with the help of different applications. Consequently, with these connections comes the requirement of security to protect personal information. Nowadays, in many applications, a biometric fingerprint recognition system has been embedded as a primary security measure. To enable a biometric fingerprint recognition system in smart mobile phones, without any additional costs, a built-in high performance camera can be utilized. The camera can capture the fingerprint image and generate biometric traits that qualify the biometric fingerprint authentication approach. However, the images acquired by a mobile phone are entirely different from the images obtained by dedicated fingerprint sensors. In this paper, we present the current trend in biometric fingerprint authentication techniques using mobile phones and explore some of the future possibilities in this field.

In this paper, two numerical methods are presented to solve an ill-posed inverse problem for Fisher's equation using noisy data. These two methods are the Haar basis and the Legendre wavelet methods combined with the Tikhonov regularization method. A sensor located at a point inside the body is used and u(x, t) at a point x = a, 0 < a < 1 is measured and these methods are applied to the inverse problem. We also show that an exponential rate of convergence of these methods. In fact, this work considers a comparative study between the Haar basis and the Legendre wavelet methods to solve some ill-posed inverse problems. Results show that an excellent estimation of the unknown function of the inverse problem which have been obtained within a couple of minutes CPU time at Pentium(R) Dual-Core CPU 2.20 GHz.

This paper focuses on the problem of robust H_∞ filtering for a class of nonlinear uncertain singular systems with time-varying delay. First of all, the definition of robust H_∞ filter is given. Considering the nonlinear disturbance link to uncertain singular systems with time-varying delay effects, the design idea of full-order robust H_∞ filter based on the Lyapunov stability theory is presented. Under the condition that nonlinear uncertain functions satisfy Lipschitz condition, the sufficient condition under which nonlinear uncertain delayed filtering error singular systems are asymptotically stable and satisfy the robust H_∞ performance is obtained by Lyapunov stability theory and linear matrix inequality (LMI) methods. Finally, two numerical examples are given to show the applicability of the proposed method.

Sequences of unit vectors for which the Kaczmarz algorithm always converges in Hilbert space can be characterized in frame theory by tight frames with constant 1. We generalize this result to the context of frames and bases. In particular, we show that the only effective sequences which are Riesz bases are orthonormal bases. Moreover, we consider the infinite system of linear algebraic equations Ax = b and characterize the (bounded) matrices A for which the Kaczmarz algorithm always converges to a solution.

The Bayesian self-organizing map (BSOM) has typically been used for density estimation. In this study, we implemented an adaptation of the model for performing unsupervized and supervised classification. In order to determine the optimal number of neurons to represent the given dataset during the learning process, an extended Bayesian learning process is proposed called the growing BSOM. It starts with two neurons and adds new neurons to the network via a process in which the neuron with the lowest individual log-likelihood is identified. The system has been tested using three synthetic datasets and one real dataset. The experimental results suggest that the BSOM-based approach can achieve better classification performance in comparisons to several widely-used models such as k-nearest neighbor (KNN), support vector machine (SVM) and Gaussian mixture model (GMM). By using the Bayesian information criterion (BIC) as a stopping criterion, the growing BSOM can model the data under study and estimate the number of clusters.

An aporia of signal de-noising is that the local signal reconstruction at the singular points. Based on the analysis for the signal singular points, combining signal scaling and orthogonal transform, This paper present a novel method called Scale-Invariant V-Transform (SIVT) for signal de-noising based on V-System, which is polynomial multi-wavelets in invariant set. SIVT employs multiple redundant basis of various scale to suppress the artifacts appearing in the singular points of denoised signal. The test results reveal the SIVT reconstructions exhibit higher visual quality and numerical measurement of SNR than wavelet-based reconstructions. Existing theory of SIVT suggests that these new approaches can perform significantly better than wavelet methods in certain signal reconstruction problems.

Having high accuracy results in data clustering and preserving the privacy of data are among the main challenges in privacy preserving clustering (PPC) techniques. High dimensionality of data is another challenge in PPC, which reduces the efficiency of the data mining algorithms. Therefore, PPC algorithms are divided into two categories. The algorithms in the first category protect the data privacy and do not reduce the data dimensionality whereas the algorithms in the second category not only preserve the data privacy but also reduce the data dimensionality. The techniques based on geometric data transformation methods (GTDMs) are related to the first category whereas the techniques based on random projection (RP), discrete cosine transform (DCT) and Haar wavelet transform (HWT) are related to the second category. The GTDMs algorithms do not reduce the data dimensionality. This is the main drawback of this algorithm which causes reduction in the performance of data mining algorithm in large datasets. The technique based on Haar wavelet transform automatically recognizes the dimensionality of the transformed data by using data energy. However, the main problem is the nature of Haar wavelet, which has one vanishing point. In this paper, we show that using Daubechies-2 wavelet, which has two vanishing points, increases the clustering quality. Therefore, to fix the drawback of the PPC algorithm based on Haar wavelet, we introduce a new algorithm to improve both the clustering quality and the privacy measure of data by using Daubechies-2 wavelet transform (D2WT). The results of experiments using several datasets, comparing the new algorithm with other existing techniques, are also presented in this paper.

A sequence of special functions in Hardy space are constructed from Cauchy kernel on unit disk 𝔻. Applying projection operator of the sequence of functions leads to an analytic sampling approximation to f, any given function in . That is, f can be approximated by its analytic samples in 𝔻^s. Under a mild condition, f is approximated exponentially by its analytic samples. By the analytic sampling approximation, a signal in can be approximately decomposed into components of positive instantaneous frequency. Using circular Hilbert transform, we apply the approximation scheme in to L^s(𝕋²) such that a signal in L^s(𝕋²) can be approximated by its analytic samples on ℂ^s. A numerical experiment is carried out to illustrate our results.

Since generalization performance of support vector machines depends a lot on parameter values of kernel functions, it is important to select optimal parameter values. How to finish optimal model selection of C-Support Vector Machines (C-SVM) with satisfiable speed is the main focus of this paper. We can hardly finish training process for large data sets with traditional methods because of long time-consuming cost. To take advantage of multi-threading and genetic algorithms, we studied a hybrid model selection method to select C and sigma of RBF kernel function for C-SVM classifier. This new method not only chooses global optimal parameters, but also saves training time based on parallel computing process. Experimental results show the efficiency and feasibility of the new method.