In this paper, we propose a novel design method of two channel critically sampled compactly supported biorthogonal graph wavelet filter banks with half-band kernels. First of all, we use the polynomial half-band kernels to construct a class of biorthogonal graph wavelet filter banks, which exactly satisfy the PR (perfect reconstruction) condition. We then present a design method of the polynomial half-band kernels with the specified degree of flatness. The proposed design method utilizes the PBP (Parametric Bernstein Polynomial), which ensures that the half-band kernels have the specified zeros at λ=2. Therefore the constraints of flatness are satisfied at both of λ=0 and λ=2, and then the resulting graph wavelet filters have the flat spectral responses in passband and stopband. Furthermore, we apply the Remez exchange algorithm to minimize the spectral error of lowpass (highpass) filter in the band of interest by using the remaining degree of freedom. Finally, several examples are designed to demonstrate the effectiveness of the proposed design method.

We proposed to apply compressed sensing to realize information sharing of link quality for wireless mesh networks (WMNs) with grid topology. In this paper, we extend the link quality sharing method to be applied for WMNs with arbitrary topology. For arbitrary topology WMNs, we introduce a link quality matrix and a matrix formula for compressed sensing. By employing a diffusion wavelets basis, the link quality matrix is converted to its sparse equivalent. Based on the sparse matrix, information sharing is achieved by compressed sensing. In addition, we propose compressed transmission for arbitrary topology WMNs, in which only the compressed link quality information is transmitted. Experiments and simulations clarify that the proposed methods can reduce the amount of data transmitted for information sharing and maintain the quality of the shared information.

This paper proposes a new class of Hilbert pairs of almost symmetric orthogonal wavelet bases. For two wavelet bases to form a Hilbert pair, the corresponding scaling lowpass filters are required to satisfy the half-sample delay condition. In this paper, we design simultaneously two scaling lowpass filters with the arbitrarily specified flat group delay responses at ω=0, which satisfy the half-sample delay condition. In addition to specifying the number of vanishing moments, we apply the Remez exchange algorithm to minimize the difference of frequency responses between two scaling lowpass filters, in order to improve the analyticity of complex wavelets. The equiripple behavior of the error function can be obtained through a few iterations. Therefore, the resulting complex wavelets are orthogonal and almost symmetric, and have the improved analyticity. Finally, some examples are presented to demonstrate the effectiveness of the proposed design method.

A novel age estimation method is presented which improves performance by fusing complementary information acquired from global and local features of the face. Two-directional two-dimensional principal component analysis ((2D)2PCA) is used for dimensionality reduction and construction of individual feature spaces. Each feature space contributes a confidence value which is calculated by Support vector machines (SVMs). The confidence values of all the facial features are then fused for final age estimation. Experimental results demonstrate that fusing multiple facial features can achieve significant accuracy gains over any single feature. Finally, we propose a fusion method that further improves accuracy.

In this paper, a design method of two-dimensional (2-D) orthogonal symmetric wavelets is proposed by using a lattice structure for multi-dimensional (M-D) linear-phase paraunitary filter banks (LPPUFB), which the authors have proposed as a previous work and then modified by Lu Gan et al. The derivation process for the constraints on the second-order vanishing moments is shown and some design examples obtained through optimization with the constraints are exemplified. In order to verify the significance of the constraints, some experimental results are shown for Lena and Barbara image.

In this paper, we propose a set of constraints for adaptive broad-band beamforming in the presence of angular errors. We first present spatial and frequency derivative constraints (SFDC) for the design of the quiescent beamformer response. With the wavelet-based blocking matrices, the proposed generalized sidelobe canceller (GSC) preserves the desired signal, and it is less sensitive to the broad-band noise. To make this beamformer more robust to the directional mismatch, we add a pseudo-interference algorithm in the weight adaptive process. Analysis and simulation results demonstrate that the angular beamwidth is insensitive to the input signal-to-noise ratio (SNR).

We present here a simple technique for parametrization of popular biorthogonal wavelet filter banks (BWFBs) having vanishing moments (VMs) of arbitrary multiplicity. Given a prime wavelet filter with VMs of arbitrary multiplicity, after formulating it as a trigonometric polynomial depending on two free parameters, we prove the existence of its dual filter based on the theory of Diophantine equation. The dual filter permits perfect reconstruction (PR) and also has VMs of arbitrary multiplicity. We then give the complete construction of two-parameter families of 17/11 and 10/18 BWFBs, from which any linear-phase 17/11 and 10/18 BWFB possessing desired features could be derived with ease by adjusting the free parameters. In particular, two previously unpublished BWFBs for embedded image coding are constructed, both have optimum coding gains and rational coef ficients. Extensive experiments show that our new BWFBs exhibit performance equal to Winger's W-17/11 and Villasenor's V-10/18 (superior to CDF-9/7 by Cohen et al. and Villasenor's V-6/10) for image compression, and yet require slightly lower computational costs.

For the performance deficiency of the pilot symbol aided channel estimation in orthogonal frequency division multiplexing (OFDM) systems, the wavelets network interpolation channel estimator is proposed. By contrast with conventional methods, wavelets network interpolation channel estimator can guarantee the high transmission rate and lower Bit error rates (BER). Computer simulation results demonstrate that the proposed channel estimation method exhibit an improved performance compared to the conventional linear channel estimation methods and is robust to fading rate, especially in fast fading channels.

Fractional calculus is the generalization of the operators of differential and integration to non-integer order, and a differential equation involving the fractional calculus operators such as d1/2/dt1/2 and d-1/2/dt-1/2 is called the fractional differential equation. They have many applications in science and engineering. But not only its analytical solutions exist only for a limited number of cases, but also, the numerical methods are difficult to solve. In this paper we propose a new numerical method based on the operational matrices of the orthogonal functions for solving the fractional calculus and fractional differential equations. Two classical fractional differential equation examples are included for demonstration. They show that the new approach is simper and more feasible than conventional methods. Advantages of the proposed method include (1) the computation is simple and computer oriented; (2) the scope of application is wide; and (3) the numerically unstable problem never occurs in our method.

A wide variety of visual textures could be successfully modeled as spatially variant by quantitatively describing them through the variation of their local spatial frequency and/or local orientation components. This class of patterns includes flow-like, granular or oriented textures. Modeling is achieved by assuming that locally, textured images contain a single dominant component describing their local spatial frequency and modulating amplitude or contrast. Spatially variant textures are non-homogeneous in the sense of having nonstationary local spectra, while remaining locally coherent. Segmenting spatially variant textures is the challenging task undertaken in this paper. Usually, the goal of texture segmentation is to split an image into regions with homogeneous textural properties. However, in the case of image regions with spatially variant textures, there is no global homogeneity present and thus segmentation passes through identification of regions with globally nonstationary, but locally coherent, textural content. Local spatial frequency components are accurately estimated using Gabor wavelet outputs along with the absolute magnitude of the convolution of the input image with the first derivatives of the underlying Gabor function. In this paper, a frequency estimation approach is used for segmentation. Indeed, at the boundary between adjacent textures, discontinuities occur in texture local spatial frequency components. These discontinuities are interpreted as corresponding to texture boundaries. Experimental results are in remarkable agreement with human visual perception, and demonstrate the effectiveness of the proposed technique.

This paper presents a new class of complex-valued compact-supported orthonormal symmlets. Firstly, some properties of complex-valued compact-supported orthonormal symmlets are investigated, and then it is shown that complex-valued symmlets can be generated by real-valued half-band filters. Therefore, the construction of complex-valued symmlets can be reduced to the design of real-valued half-band filters. Next, a design method of real-valued half-band FIR filters with some flatness requirements is proposed. For the maximally flat half-band filters, a closed-form solution is given. For the filter design with a given degree of flatness, the design problem is formulated in the form of linear system by using the Remez exchange algorithm and considering the given flatness condition. Therefore, a set of filter coefficients can be easily computed by solving a set of linear equations, and the optimal solution is obtained through a few iterations. Finally, some design examples are presented to demonstrate the effectiveness of the proposed method.

In this letter we propose a filter for extracting a quasi-periodic signal from a noisy observation using wavelets. It is assumed that the instantaneous frequency of the signal is known. A particularly difficult task when the frequency and amplitude of the desired signal are varying with time is shown. The proposed algorithm is compared with three other methods.

This paper introduces the construction of a family of complex-valued scaling functions and wavelets with symmetry/antisymmetry, compact support and orthogonality from the Daubechies polynomial, and applies them to solve electromagnetic scattering problems. For simplicity, only two extreme cases in the family, maximum-localized complex-valued wavelets and minimum-localized complex-valued wavelets are investigated. Regularity of root location of the Daubechies polynomial in spectral factorization are also presented to construct these two extreme genus of complex-valued wavelets. When wavelets are used as basis functions to solve electromagnetic scattering problems by the method of moment (MoM), they often lead to sparse matrix equations. We will compare the sparsity of MoM matrices by the real-valued Daubechies wavelets, minimum-localized complex-valued Daubechies and maximum-localized complex-valued Daubechies wavelets. Our research summarized in this paper shows that the wavelets with smaller signal width will result in a more sparse MoM matrix, especially when the scatterer is with many corners.

An approximate scheme for decomposing and reconstructing a continuous-time signal as a linear combination of the B-splines is studied. It is an oversampling discrete-time implementation derived by substituting the multifold RRS functions for the B-splines. The RRS functions are multifold discrete convolution of the sampled rectangular functions. Analysis of the scheme yields conditions for the circuit parameters to assure stability and required precision. A design example is presented that makes the error less than 1% in the supremal norm by the oversampling ratio of 512. Its numerical simulation is also presented.

Research in very low-bit rate coding has made significant advancements in the past few years. Most recently, the introduction of the MPEG-4 proposal has motivated a wide variety of a approaches aimed at achieving a new level of video compression. In this paper we review progress in VLBV categorized into 3 main areas. (1) Waveform coding, (2) 2D Content-based coding, and (3) Model-based coding. Where appropriate we also described proposals to the MPEG-4 committee in each of these areas.

Fast wavelet transform is presented for realtime processing of wavelet transforms. A processor for the fast wavelet transform is of the frequency sampling structure in architectural level. The fast wavelet transform owes its parallelism both to the frequency sampling structure and parallel tapping of a series of delay elements. Computational burden of the fast transform is hence independent of specific scale values in wavelets and the parallel processing of the fast transform is readily implemented for real-time applications. This point is quite different from the computation of wavelet transforms by convolution. We applied the fast wavelet transform to detecting detonation in a vehicle engine for precise real-time control of ignition advancement. The prototype wavelet for this experiment was the Gaussian wavelet (i.e. Gabor function) which is known to have the least spread both in time and in frequency. The number of complex multiplications needed to compute the fast wavelet transform over 51 scales is 714 in this experiment, which is less than one tenth of that required for the convolution method. Experimental results have shown that detonation is successfully detected from the acoustic vibration signal picked up by a single knock sensor embedded in the outer wall of a V/8 engine and is discriminated from other environmental mechanical vibrations.