International Journal of Wavelets, Multiresolution and Information Processing

This paper investigates the applicability of the constructive approach proposed in Ref. 1 to wavelet neural networks (WNN). In fact, two incremental training algorithms will be presented. The first one, known as one pattern at a time (OPAT) approach, is the WNN version of the method applied in Ref. 1. The second approach however proposes a modified version of Ref. 1, known as one epoch at a time (OEAT) approach. In the OPAT approach, the input patterns are trained incrementally one by one until all patterns are presented. If the algorithm gets stuck in a local minimum and could not escape after a fixed number of successive attempts, then a new wavelet called also wavelon, will be recruited. In the OEAT approach however, all the input patterns are presented one epoch at a time. During one epoch, each pattern is trained only once until all patterns are trained. If the resulting overall error is reduced, then all the patterns will be retrained for one more epoch. Otherwise, a new wavelon will be recruited. To guarantee the convergence of the trained networks, an adaptive learning rate has been introduced using the discrete Lyapunov stability theorem.

In this paper we propose a new type of non-negative time-frequency distribution associated with mono-components in both the non-periodic and periodic cases, called transient time-frequency distribution (TTFD), and study its properties. The TTFD of a mono-component signal can be obtained directly through its analytic instantaneous frequency. The characteristic property of TTFD is its complete concentration along the analytic instantaneous frequency graph. For multi-components there are induced time-frequency distributions called composing transient time-frequency distribution (CTTFD). Each CTTFD is defined as the superposition of the TTFDs of the composing intrinsic mono-components in a suitable mono-components decomposition of the targeted multi-component. In studying the properties of TTFD and CTTFD the relations between the Fourier frequency and analytic instantaneous frequency are examined.

This paper presents a construction method of bivariate N-band wavelet tight frames. First, we discuss the properties of N-band scaling functions, and the construction of the corresponding wavelet tight frame as well as the explication of the formula of the wavelet tight frame. Thereafter, the decomposition and reconstruction formulas of the bivariate N-band wavelet tight frames are provided. Finally, the numerical example is given.

Morais has recently introduced certain complete orthogonal sets of monogenic polynomials over 3D prolate spheroids with remarkable properties. The underlying functions take on either values in the reduced and full quaternions (identified, respectively, with ℝ³ and ℝ⁴), and are generally assumed to be nullsolutions of the well known Riesz and Moisil–Théodoresco systems in ℝ³. In continuation of these studies, we recall some fundamental properties of the polynomials, and prove some recursive formulae between them. As a consequence, we obtain a two-term type recurrence relation satisfied by those basis polynomials. These results are then employed to investigate a rather wide class of approximation properties for monogenic functions over 3D prolate spheroids in terms of spheroidal monogenics.

To desire expectable applications in image processing, the construction of 3-band dual tree complex wavelet is a meaningful and constructive topic. In this paper, a sufficient and necessary condition 2π/3-periodic of phase difference between the prime and dual filter banks is proposed. With this condition, it is proposed that the phase function θ_l(ω) of wavelet filters can be uniquely determined by the phase function θ₀(ω) of the scaling filters. Imposed on a necessary constraint to θ₀(ω), phase function θ_l(ω) can be obtained which results in the analytical of the 3-band dual tree complex wavelet. Furthermore, the complex filter banks are obtained using the wavelet matrix factorization approach. Then the dual tree 3-band complex wavelet is analytical that indicates approximately shift invariance property. In addition, it also has more direction selectivity because there are more sub-bands than dyadic wavelet transform is frequency domain.

In this paper, we propose an expression for estimating the byte loss probability in a single server link taking into account the multifractal properties of network traffic. Using the proposed loss probability estimation approach, we present an adaptive transmission rate control scheme for network communication servers. The proposed algorithm includes a search algorithm in order to find the rate that attains the required loss probability in a network communication link. Finally, we compare the proposed multifractal based adaptive rate allocation to a monofractal based dynamic allocation scheme present in the literature.

This paper develops an adaptive output feedback controller that forces an autonomous underwater vehicle (AUV), named Omni-Directional Intelligent Navigator (ODIN), to track a desired trajectory with bounded errors in wave disturbance condition. An adaptive controller is introduced based on a nonlinear model whose measurable output is corrupted by wave disturbances. Thus an observer is built to reconstruct the full states including wave velocity, wave motion displacement, vehicles velocity, position and rotation angle information which are used in the output feedback controller. Ultimate boundedness of the error signals is shown through Lyapunovs direct method. Finally, simulation studies for ODIN illustrate the effectiveness of the proposed control scheme.

Skype is one of the most popular video call services in the current Internet world. One of its strengths is the use of an adaptive mechanism to match the constraints of the underlying network. This work is focused on how this mechanism can maximize the video quality as perceived by the viewers using objective assessment methods. We built a testbed to stream certain video sequences through Skype between two clients over impaired communication channels. Original and recorded videos were compared to assess the achieved quality. Extensive experimentation has shown that Skype has problems when transmitting high motion videos and especially complex videos with frequent interchange between frames of low and high temporal information. The results suggest that random packet loss intensifies quality degradation for those videos more than packet loss bursts or jitter.

Sparse LS-SVM yields better generalization capability and reduces prediction time in comparison to full dense LS-SVM. However, both methods require careful selection of hyper-parameters (HPS) to achieve high generalization capability. Leave-One-Out Cross Validation (LOO-CV) and k-fold Cross Validation (k-CV) are the two most widely used hyper-parameter selection methods for LS-SVMs. However, both fail to select good hyper-parameters for sparse LS-SVM. In this paper we propose a new hyper-parameter selection method, LGEM-HPS, for LS-SVM via minimization of the Localized Generalization Error (L-GEM). The L-GEM consists of two major components: empirical mean square error and sensitivity measure. A new sensitivity measure is derived for LS-SVM to enable the LGEM-HPS select hyper-parameters yielding LS-SVM with smaller training error and minimum sensitivity to minor changes in inputs. Experiments on eleven UCI data sets show the effectiveness of the proposed method for selecting hyper-parameters for sparse LS-SVM.

In this paper, we introduce a sparse recovery strategy for analytic signals in Hardy space H²(𝔻), where 𝔻 denotes the unit disk of the complex plane. The representation strategy is based on the optimization technique. We investigate the asymptotic singular values distribution of the dictionary matrix and give an estimation of the number of rows of the random matrix. To the best of our knowledge, this is the first time that such result is given. This result demonstrates that the dictionary of the normalized Szegö kernels (or reproducing kernels) is perfect for decompositions of analytic signals. A numerical example is presented exhibiting the theory. As applications, we still work on time-frequency analysis and propose a new type of non-negative time-frequency distribution associated with mono-components in the periodic case.