International Journal of Wavelets, Multiresolution and Information Processing

A frame can be completed to a tight frame by adding some additional vectors. However, for the purpose of computational efficiency, we need to put restrictions to the number of added vectors. In this paper we propose a constructive method that allows to extend a given frame to an oblique dual frame pair such that the number of added vectors is in general much smaller than the number of added vectors used to extend it to a tight frame. We also present a uniqueness characterization and several equivalent characterizations for an oblique dual frame pair, it turns out that oblique dual frame pair provides more flexibilities than alternate dual frame pair.

The conventional multiple component image compression approach separates the input image into several components, each of which is predicted and encoded independently. This approach creates redundancy because the prediction methods as well as the residual subcomponents must be transmitted. In this paper, we propose a new multiple-component predictive coding framework. First, we separate the reconstructed image into several subcomponents. Then, we use the previously encoded subcomponent to predict the current block, and then combine the prediction residuals of each subcomponent. To separate an image into multiple subcomponents, we designed a fast operator-based image separation algorithm. The numerical results demonstrate that the algorithm outperforms the H.264/AVC intra-frame prediction algorithm and the JPEG2000 algorithm on images with ample textures.

This paper addresses vector-valued subspace Gabor frames with rational time-frequency product. By introduction of a suitable Zak transform matrix, we characterize vector-valued subspace Gabor frames, Riesz bases and orthonormal bases. We characterize the uniqueness of Gabor duals of type I and type II. Using the uniqueness results, we extend the classical Balian-Low theorem to vector-valued subspace Gabor frames. We also point out Ron-Shen duality principe does not hold for a general vector-valued subspace Gabor frame.

We construct smooth nonseparable compactly supported refinable functions that generate multiresolution analyses on L²(ℝ^d), d > 1. Using these refinable functions we construct smooth nonseparable compactly supported orthonormal wavelet systems. These systems are nonseparable, in the sense that none of its constituent functions can be expressed as the product of two functions defined on lower dimensions. Both the refinable functions and the wavelets can be made as smooth as desired. Estimates for the supports of these scaling functions and wavelets, are given.

In this work, a new Wavelet–Galerkin method for boundary value problems is presented. It improves the approximation in terms of scaling functions obtained through a collocation scheme combined with variational equations. A B-spline multiresolution structure on the interval is designed in order to refine the solution recursively and efficiently using wavelets. Numerical examples are given to verify good convergence properties of the proposed method.

A new approach for feature extraction using neural response has been developed in this paper through combining the hierarchical architectures with the sparse coding technique. As far as proposed layered model, at each layer of hierarchy, it concerned two components that were used are sparse coding and pooling operation. While the sparse coding was used to solve increasingly complex sparse feature representations, the pooling operation by comparing sparse outputs was used to measure the match between a stored prototype and the input sub-image. It is recommended that value of the best matching should be kept and discarding the others. The proposed model is implemented and tested taking into account two ranges of recognition tasks i.e. image recognition and speech recognition (on isolated word vocabulary). Experimental results with various parameters demonstrate that proposed scheme leads to extract more efficient features than other methods.

A two-dimensional stochastic point process can be regarded as a random measure and thus represented as a (countable) sum of Delta Dirac measures concentrated at some points. Integration with respect to the point process itself leads to the concept of the continuous wavelet transform of a point process. Applying then suitable translation, rotation and dilation operations through a non unitary operator, we obtain a transformed point process which highlights main properties of the original point process. The choice of the mother wavelet is relevant and we thus conduct a detailed analysis proposing three two-dimensional mother wavelets. We use this approach to detect main directions present in the point process, and to test for anisotropy.

A design method of an optimal preview controller for a class of linear continuous time-varying systems is presented in this paper. By differentiating both the output error signal and the two sides of the state equation, an augmented error system is constructed, which contains the error signal, the state vector and the derivative of the state vector. Then the performance index function is introduced and the control problem is solved by optimal control theory. Thus the optimal preview control input for the original time-varying system is found. The proposed controller includes the previewable future signal, so the response speed is accelerated. Meanwhile, the integrators in the controller make the output vector track the target signal better. The numerical simulations illustrate the validity of the proposed method.

In this paper, we apply wavelet optimized finite difference method to solve modified Camassa–Holm and modified Degasperis–Procesi equations. The method is based on Daubechies wavelet with finite difference method on an arbitrary grid. The wavelet is used at regular intervals to adaptively select the grid points according to the local behaviour of the solution. The purpose of wavelet-based numerical methods for solving linear or nonlinear partial differential equations is to develop adaptive schemes, in order to achieve accuracy and computational efficiency. Since most of physical and scientific phenomena are modeled by nonlinear partial differential equations, but it is difficult to handle nonlinear partial differential equations analytically. So we need approximate solution to solve these type of partial differential equation. Numerical results are presented for approximating modified Camassa–Holm and modified Degasperis–Procesi equations, which demonstrate the advantages of this method.

Various wearable computing devices face problems with their power supplies, communication channels, and placement. Conductive clothes can resolve these problems, but it is still difficult to know the positions of devices on the conductive fabric. Therefore, we propose a method to detect the positions of such devices by using a camera. To detect the positions, our method blinks the LEDs on the devices according to their ID. Additionally, we propose several methods to shorten the time for detection. An experimental evaluation confirmed that compared with conventional method our methods reduce the time to detect the positions of the devices.