International Journal of Wavelets, Multiresolution and Information Processing

In this paper, we present an efficient biorthogonal wavelet construction for the ternary Loop subdivision based on the lifting scheme, and give the corresponding decomposition and reconstruction formulas. We apply the proposed algorithm to the progressive transmission and the denoising of 3D graphics, and show its sufficient stability and good performance by some numerical experiments. Since the usual input mesh does not possess the property of subdivision connectivity, while the multiresolution analysis based on subdivision surface requires the processed initial mesh to be semi-regular, we further propose a new rapid algorithm of constructing the initial mesh which not only possesses ternary subdivision connectivity but also approximates the given input mesh.

A main issue in machine learning research is to analyze the generalization performance of a learning machine. Most classical results on the generalization performance of regularization algorithms are derived merely with the complexity of hypothesis space or the stability property of a learning algorithm. However, in practical applications, the performance of a learning algorithm is not actually affected only by an unitary factor just like the complexity of hypothesis space, stability of the algorithm and data quality. Therefore, in this paper, we develop a framework of evaluating the generalization performance of regularization algorithms combinatively in terms of hypothesis space complexity, algorithmic stability and data quality. We establish new bounds on the learning rate of regularization algorithms based on the measure of uniform stability and empirical covering number for general type of loss functions. As applications of the generic results, we evaluate the learning rates of support vector machines and regularization networks, and propose a new strategy for regularization parameter setting.

Multiple description coding is one of the source coding techniques used to alleviate the problems of packet loss in network. The objective is to encode a source into two (or more) bitstreams supporting two quality levels of decoding: A high-quality reconstruction decoded from the two bitstreams together, and two lower ones, but still acceptable, decoded from either of the two bitstreams individually. Most of the earlier works concentrated on the trade-off between redundancy and average side distortion, which is insufficient to evaluate the system performance. In this paper, we discuss the difference in quality between the two side reconstructions, which is defined as the balance eccentric modulus of the coding system. A scenario to design balanced multiple description coding system is presented. Application to the popular first-order autoregressive model yields encouraging results.

In this paper, we provide an asymptotic expression for mean integrated squared error (MISE) of nonlinear wavelet density estimator for a truncation model. It is assumed that the lifetime observations form a stationary α-mixing sequence. Unlike for kernel estimator, the MISE expression of the nonlinear wavelet estimator is not affected by the presence of discontinuities in the curves. Also, we establish asymptotic normality of the nonlinear wavelet estimator.

A generic technique for construction of ternary interpolatory subdivision schemes, which is based on polynomial and discrete splines, is presented. These schemes have rational symbols. The symbols are explicitly presented in the paper. This is accompanied by a detailed description of the design of the refinement masks and by algorithms that verify the convergence of these schemes. In addition, the smoothness of the limit functions is investigated. The ternary subdivision schemes, whose construction is based on continuous splines, become tools for fast computation ofıory s of arbitrary order at triadic rational points.

Dirac is a hybrid motion-compensated state-of-the-art video codec that can be used without the payment of license fees. It can be easily adapted for new platforms and is aimed at applications ranging from HDTV to web streaming. The objective of this paper is to analyze Dirac video codec based on several input test sequences, and compare its performance with H.264/MPEG-4 Part 10 AVC. Both Dirac and H.264 are implemented using different video test sequences at various constant "target" bit rates ranging from 10 KBps to 200 KBps at image resolutions from QCIF to SD. The results have been recorded graphically and we arrive at a conclusion whether Dirac's performance is comparable to H.264. We also research whether Dirac outperforms H.264/MPEG-4 Part 10 in terms of computational speed and efficiency.

This paper studies the preview control problem for continuous-time control systems. A design method for an optimal preview controller is presented, when the desired tracking and disturbance are piecewise-continuously differentiable functions. Applying the same techniques as for optimal control in linear quadratic optimal control, we derive a type-one servomechanism with both desired tracking preview and disturbance preview compensation. A proof is presented that if the original system is stabilizable and detectable, the closed-loop system is asymptotically stable. We also design a full-dimensional state observer for the considered system. Finally, numerical simulations show the efficiency of the controller.

The almost everywhere convergence of wavelets transforms of L_p-functions under minimal conditions on wavelets is well known. But this result does not provide any information about the exceptional set (of Lebesgue measure zero), where convergence does not hold. In this paper, under slightly stronger conditions on wavelets, we prove convergence of wavelet transforms everywhere on the entire Lebesgue set of L_p-functions. On the other hand, practically all the wavelets, including Haar and "French hat" wavelets, used frequently in applications, satisfy our conditions. We also prove that the same conditions on wavelets guarantee the Riemann localization principle in L₁ for the wavelet transforms.