International Journal of Wavelets, Multiresolution and Information Processing

In this paper, we develop a priori and a posteriori error estimates for wavelet-Taylor–Galerkin schemes introduced in Refs. 6 and 7 (particularly wavelet Taylor–Galerkin scheme based on Crank–Nicolson time stepping). We proceed in two steps. In the first step, we construct the priori estimates for the fully discrete problem. In the second step, we construct error indicators for posteriori estimates with respect to both time and space approximations in order to use adaptive time steps and wavelet adaptivity. The space error indicator is computed using the equivalent norm expressed in terms of wavelet coefficients.

In this paper, a selective curvelet coefficient digital watermarking algorithm is proposed. Traditionally, curvelet watermarks are embedded into all sample frequency bands. However, the study of individual band behavior and the use of single band for watermarking have not been reported. The selective band will provide an addition security feature against any physical tampering. This paper aims to give an intensive study on the robustness of watermarking using selective curvelet coefficients from a single band and to find out the best band for embedding watermark. Wrapping of specially selected Fourier samples is employed to implement Fast Discrete Curvelet Transforms (FDCT) to transform the digital image to the curvelet domain.

In recent years, significant advances in vibration control of structures have been achieved due greatly to the emergent technologies based on smart materials, such as mangnetorheological (MR) fluids. This paper develops a computational algorithm for the modeling and identification of the MR dampers by using wavelet systems to handle the nonlinear terms. By taking into account the Haar wavelets, the properties of integral operational matrix and of product operational matrix are introduced and utilized to find an algebraic representation form instead of the differential equations of the dynamical system. It is shown that MR damper parameters can be estimated easily by considering only the algebraic equations obtained.

Linear Discriminant Analysis (LDA) is a popular statistical method for both feature extraction and dimensionality reduction in face recognition. The major drawback of LDA is the so-called small sample size (3S) problem. This problem always occurs when the total number of training samples is smaller than the dimension of feature space. Under this situation, the within-class scatter matrix S_w becomes singular and LDA approach cannot be implemented directly. To overcome the 3S problem, this paper proposes a novel wavelet-face based subspace LDA algorithm. Wavelet-face feature extraction and dimensionality reduction are based on two-level D4-filter wavelet transform and discarding the null space of total class scatter matrix S_t. It is shown that our obtained projection matrix satisfies the uncorrelated constraint conditions. Hence in the sense of statistical uncorrelation, this projection matrix is optimal. The proposed method for face recognition has been evaluated with two public available databases, namely ORL and FERET databases. Comparing with existing LDA-based methods to solve the 3S problem, our method gives the best performance.

In this paper, we propose two novel invariant algorithms for pattern recognition by using ridgelet packets and the Fourier transform. Ridgelet packets provide many orthonormal bases that can effectively capture directional features present in pattern images. The Fourier transform is good at eliminating the orientation differences. By combining these two tools, very efficient rotation invariant pattern recognition techniques are created. Experimental results show that the proposed methods achieve very high classification rates and they outperform other state-of-the-art methods for rotation invariant pattern recognition under both noise-free and noisy environments.

Generally, for face recognition, image shift and rotation problems must be addressed. The "ring rotation invariant transform" technique is used to transfer geometrical features of face image to other more salient ones; by which one can identify whether a sample or unknown image is the identical image. It also can solve image rotation problem. To deal with the image-shifting problem, this study uses one pixel inside a sample image to compare with the corresponding pixels in the unknown image to locate the closest matching point. In this study, three different kinds of extracted ring signals are generated, which are (1) ring-radius-31, (2) ring-radius-22, and (3) ring-radius-13. These signals are used to generate the rotation invariant magnitudes and several magnitudes are combined as one entity and, subsequently, saved inside one specific corresponding pixel in the BMP file. By this approach, one pixel will possess more geometrical-features of the face images; one entity in sample image is compared with entities inside the corresponding radius-6-cake area of the unknown image to locate the closest matching point.

In this paper, the properties of multiresolution analysis on the product of Heisenberg group are investigated. Moreover, orthonormal Haar wavelet bases for L²(ℋⁿ) are constructed.