International Journal of Wavelets, Multiresolution and Information Processing

This paper explores the scope of integer wavelets in watermarking on compressed image with the aid of convolution coding as channel coding. Convolution coding is applied on compressed host data, instead of its direct application on watermark signal as used widely for robustness improvement in conventional system. Two-fold advantages, namely flexibility in watermarking through the creation of redundancy on the compressed data as well as protection of watermark information from additive white Gaussian noise (AWGN) attack are achieved. Integer wavelet is used to decompose the encoded compressed data that leads to lossless processing and creation of correlation among the host samples due to its mathematical structure. Watermark information is then embedded using dither modulation (DM)-based quantization index modulation (QIM). The relative gain in imperceptibility and robustness performance are reported for direct watermark embedding on entropy decoded host, using repetition code, convolution code, and finally the combined use of channel codes and integer wavelets. Simulation results show that 6.24 dB (9.50 dB) improvement in document-to-watermark ratio (DWR) at watermark power 12.73 dB (16.81 dB) and 15 dB gain in noise power for watermark decoding at bit error rate (BER) of 10^-2 are achieved, respectively over direct watermarking on entropy decoded data.

For the smooth surface of rotation class M, the explicit construction of two local flattening maps p are given. By virtue of the inverse projection p^-1, where the bijection projection p is the local flattening map from a two-dimensional smooth surface M of rotation class to a plane, the local wavelet transform on M can be generated from wavelet transform on a plane. For the two examples of the quadratic parameter rotation surface and parabolic general rotation surface, by using the two local flattening maps p respectively, the construction of the local dilation is systematically studied, and local wavelet transform of them is offered. We also show the local wavelet graphical representation on the quadratic parameter rotation surface and parabolic general rotation surface. Finally, the inverse transform formula of the local wavelet transform, that is, the reconstruction formula is also offered.

Locality-preserving projection (LPP) is a promising manifold-based dimensionality reduction and linear feature extraction method for face recognition. However, there exist two main issues in traditional LPP algorithm. LPP does not utilize the class label information at the training stage and its performance will be affected for classification tasks. In addition, LPP often suffers from small sample size (3S) problem, which occurs when the dimension of input pattern space is greater than the number of training samples. Under this situation, LPP fails to work. To overcome these two limitations, this paper presents a novel supervised regularization LPP (SRLPP) approach based on a supervised graph and a new regularization strategy. It theoretically proves that regularization matrix approaches to the original one as the regularized parameter tends to zero. The proposed SRLPP method is subsequently applied to face recognition. The experiments are conducted on two publicly available face databases, namely ORL database and FERET database. Compared with some existing LDA-based and LPP-based linear feature extraction approaches, experimental results show that our SRLPP approach gives superior performance.

In this paper, an orthogonal wavelet transform of signal based on complex B-spline bases is given. The new wavelet transform realizes accurate computation of coefficients of complex B-spline base functions. It integrates good properties of orthogonality, symmetry and continuity, and offers better approximations to continuous signal than do the Haar wavelet and Daubechies wavelets. All algorithms of the new orthogonal wavelet transform are based on explicit formulas and easy to be implemented.

Most dimensionality reduction methods depend significantly on the distance measure used to compute distances between different examples. Therefore, a good distance metric is essential to many dimensionality reduction algorithms. In this paper, we present a new dimensionality reduction method for data visualization, called Distance-ratio Preserving Embedding (DrPE), which preserves the ratio between the pairwise distances. It is achieved by minimizing the mismatch between the distance ratios derived from input and output space. The proposed method can preserve the relational structures among points of the input space. Extensive visualization experiments compared with existing dimensionality reduction algorithms demonstrate the effectiveness of our proposed method.

A multivariate calibration method with support vector regression based on random projection is proposed. The proposed algorithm reduces the dimensionality of high-dimensional spectral data by random projection, and then performs quantitative calibration using support vector regression. Support vector regression method can handle nonlinear regression which is usually encountered in spectral analysis. Moreover, model calculation and optimization on the projected data are relatively fast. A comparative study of the proposed method and partial least squares on four spectral datasets is presented. The proposed method allows drastic reduction in data size and computing time, while preserving the predict performance.

In this paper, a wavelet-based approach is presented for estimation of vehicle modal parameters. The acceleration of a colliding vehicle is measured in its center of gravity — this crash pulse contains detailed information about vehicle behavior throughout a collision. Three types of signal analysis are elaborated here: time domain analysis (i.e. description of kinematics of a vehicle in time domain), the frequency analysis (identification of the parameters of the crash pulse in frequency domain), and the time-frequency analysis, which comprises those techniques that study a signal in both the time and frequency domains simultaneously, using Morlet wavelet properties. The frequency components of the recorded crash pulse are identified by determining the ridge of the wavelet coefficients matrix. Having knowledge of the natural frequency of the signal, the damping factor for a given mode shape of the signal is estimated. In this work the major frequencies of the crash pulse are determined and the damping factor for the major mode shape is identified. The comparative analysis between the current method's outcome, the response of a model established previously by using different approach and the behavior of a real car is performed and reliability of the actual methods and tools is evaluated.

In human body pose estimation, manifold learning has been considered as a useful method with regard to reducing the dimension of 2D images and 3D body configuration data. Most commonly, body pose is estimated from silhouettes derived from images or image sequences. A major problem in applying manifold estimation to pose estimation is its vulnerability to silhouette variation caused by changes of factors such as viewpoint, person, and distance.

In this paper, we propose a novel approach that combines three separate manifolds for viewpoint, pose, and 3D body configuration focusing on the problem of viewpoint-induced silhouette variation. The biased manifold learning is used to learn these manifolds with appropriately weighted distances. The proposed method requires four mapping functions that are learned by a generalized regression neural network for robustness. Despite the use of only three manifolds, experimental results show that the proposed method can reliably estimate 3D body poses from 2D images with all learned viewpoints.

In this paper, a convergent method based on Generalized Iterative Scaling (GIS) with staggered Aitken acceleration is proposed to estimate the parameters for an on-line Conditional Random Field (CRF). The staggered Aitken acceleration method, which alternates between the acceleration and non-acceleration steps, ensures computational simplicity when analyzing incomplete data. The proposed method has the following advantages: (1) It can approximate parameters close to the empirical optimum in a single pass through the training examples; (2) It can reduce the computing time by approximating the Jacobian matrix of the mapping function and estimating the relation between the Jacobian and Hessian in order to replace the inverse of the objective function's Hessian matrix. We show the convergence of the penalized GIS based on the staggered Aitken acceleration method, compare its speed of convergence with those of other stochastic optimization methods, and illustrate experimental results with two public datasets.

The discrete wavelet transform; depending of the pair of integers (m, n), applied to functions f in L²(R) with respect to an admissible function h in L²(R) of class C^∞ with compact support, is used to prove that f is continuous at x = 0, and furthermore at any x = b in R if and only if there exists the convergence of the discrete wavelet transform, as (m, n) → (-∞, n₁) for any integer n₁.