International Journal of Wavelets, Multiresolution and Information Processing

In this paper, we propose a new family of perfect reconstruction (PR) complex filter banks, named interleaved discrete Fourier transform modulated filter banks (Interleaved DFT-FBs). In the filter banks, the analysis filters are generated by interlaced exponential modulating two different analysis prototype filters, and the synthesis filters are generated by two different synthesis prototype filters via the same manner. The filter banks have a simple polyphase structure similar to DFT modulated filter banks (DFT-FBs). More importantly, the proposed Interleaved DFT-FBs can achieve critically sampled PR complex filter bank with FIR analysis and synthesis filters, which is impossible for DFT-FBs. We give and prove the PR condition for 2M-band Interleaved DFT-FBs. Utilizing the result, the design procedure of the prototype filters is presented. In addition, by the theoretic analysis and numerical examples, it is shown that the analysis and synthesis filters cannot simultaneously provide good stopband attenuation for the critically sampled PR Interleaved DFT-FBs. Although the limitation always exits, the filter banks can find applications in some subband coding systems of high bit rate.

This paper constructs a class of semi-orthogonal and bi-orthogonal wavelet transforms on possibly irregular point sets with the property that the scaling coefficients are independent from the order of refinement. That means that scaling coefficients at a given scale can be constructed with the configuration at that scale only. This property is of particular interest when the refinement operation is data dependent, leading to adaptive multiresolution analyses. Moreover, the proposed class of wavelet transforms are constructed using a sequence of just two lifting steps, one of which contains a linear interpolating prediction operator. This operator easily allows extensions towards directional offsets from predictions, leading to an edge-adaptive nonlinear multiscale decomposition.

Image quality is a key characteristic in image processing,^10,11 image retrieval,^12,13 and biometrics.¹⁴ In this paper, a novel reduced-reference image quality assessment method is proposed based on wavelet transform. By simulating the human visual system, we take the variance of the visual sensitive coefficients into account to measure a distorted image. The computational complexity of the proposed method is much lower compared with some existing methods. Experimental results demonstrate its advantages in terms of correlation coefficient, outlier ratio, transmitted information, and CPU cost. Moreover, it is also illustrated that the proposed method has a good accordance with human subjective perception.

It is well known that the distribution of the discrete cosine transform (DCT) coefficients of most natural images follow a Laplace distribution. In this note, a collection of formulas is derived for the distribution of the actual DCT coefficient. The corresponding estimation procedures are derived by the method of moments and the method of maximum likelihood. Finally, the superior performance of the derived distributions over the standard Laplace model is illustrated. It is expected that this work could serve as a useful reference and lead to improved modeling with respect to image analysis and image coding.

The paper is concerned with the application of wavelet-based neural networks for optimal control of robotic manipulators motion. The model of robotic manipulators with regard to frictions and disturbances is nonlinear and uncertain. Optimal control law is found by the optimization of the Hamilton–Jacobi–Bellman (H-J-B) equation and it shows how wavelet-based neural networks can overcome nonlinearities through optimization without preliminary off-line learning phase. The neural network is learned as on-line and an adaptive learning algorithm is derived from the Lyapunov theory. This is so that both tracking stability and error convergence of the estimation for the nonlinear function can be guaranteed in the closed-loop system. The Lyapunov function for the nonlinear analysis is derived from the user input in terms of a specified quadratic performance index. Simulation results on a three-link robot manipulator show the satisfactory performance of the proposed control schemes even in the presence of large modeling uncertainties and external disturbances. Furthermore, it is shown that the tracking error for wavelet neural networks is less than conventional neural networks.

The fusion of wavelet technique and support vector machines (SVMs) has become an intensive study in recent years. Considering that the wavelet technique is the theoretical foundation of multiresolution analysis (MRA), it is valuable for us to investigate the problem of whether a good performance could be obtained if we combine the MRA with SVMs for signal approximation. Based on the fact that the feature space of SVM and the scale subspace in MRA can be viewed as the same Reproducing Kernel Hilbert Spaces (RKHS), a new algorithm named multiresolution signal decomposition and approximation based on SVM is proposed. The proposed algorithm which approximates the signals hierarchically at different resolutions, possesses better approximation of smoothness for signal than conventional MRA due to using the approximation criterion of the SVM. Experiments illustrate that our algorithm has better approximation of performance than the MRA when being applied to stationary and non-stationary signals.

While in the process of decomposition of the Mallat discrete wavelet transform (DWT) fast algorithm, the algorithm has a drawback, that is, there is frequency distortion in the high frequency subband. In this paper, a new algorithm of decomposition and reconstruction in the discrete wavelet is presented. The algorithm can solve the frequency distortion in the high frequency subband in the process of decimation in each level. The simulation of numerical value example tests the validity of the algorithm.

The parametrization for two kinds of multifilter banks generating balanced multiwavelets is presented in this paper. In case (I), both lowpass and highpass filters are flipping filters. Filters in case (II) have different lengths, and both lowpass and highpass filters are symmetric (antisymmetric). Based on these parametric expressions, some balanced multiwavelets and analysis-ready multiwavelets (armlets) are constructed. Moreover, the application of these multiwavelets constructed in image processing is also studied.

The notion of multiple vector-valued wavelet packets is introduced. A procedure for constructing the multiple vector-valued wavelet packets is presented. Their characteristics are investigated by means of integral transformation and operator theory, and three orthogonality formulas concerning the multiple vector-valued wavelet packets. Finally, new orthogonal bases of L²(R, C^{s × s}) are constructed from these multiple vector-valued wavelet packets.

Nowadays, digital watermarking algorithms are widely applied to ownership protection and tampering detection of digital images. In this paper, a new reversible watermarking algorithm based on wavelet lifting scheme is proposed. In the algorithm, the image is firstly divided into some no-overlapping blocks, and then the wavelet lifting scheme where on every block, is performed watermarking data is embedded into the image according to the attribute of the subband of every block. In order to guarantee the security of algorithm, chaotic system is used to shuffle the position of blocks. The interesting point and usefulness of the algorithm lies in the fact that the watermarked image can be exactly restored into the original image, and the watermarking is robust to cropping. The experimental results show the effectiveness of this scheme.

Recently, the use of wavelet transform has led to significant advances in image denoising applications. Among wavelet-based denoising approaches, the Bayesian techniques give more accurate estimates. Considering interscale dependencies, these estimates become closer to the original image. In this context, the choice of an appropriate model for wavelet coefficients is an important issue. The performance can also be improved by estimating model parameters in a local neighborhood. In this paper, we propose the bivariate normal inverse Gaussian (NIG) distribution, which can model a wide range of heavy-tailed to less heavy-tailed processes, to model the local wavelet coefficients at adjacent scales. We will show that this new statistical model is superior to the conventional generalized Gaussian (GG) model. Then, a minimum mean square error-based (MMSE-based) Bayesian estimator is designed to effectively remove noise from wavelet coefficients. Exploiting this new statistical model in the dual-tree complex wavelet domain, we achieved state-of-the-art performance among related recent denoising approaches, both visually and in terms of peak signal-to-noise ratio (PSNR).