International Journal of Wavelets, Multiresolution and Information Processing

This paper investigates how the mean envelope, the subtrahend in the sifting procedure for the Empirical Mode Decomposition (EMD) algorithm, represents as an expansion in terms of basis. To this end, a novel approach that gives an alternative analytical expression using B-spline functions is presented. The basic concept lies mainly on the idea that B-spline functions form a basis for the space of splines and have refined-node representations by knot insertion. This newly-developed expression is essentially equivalent to the conventional one, but gives a more explicit formulation on this issue. For the purpose of establishing the mathematical foundation of the EMD methodology, this study may afford a favorable opportunity in this direction.

In this paper, we introduce a family of real-valued functions which have spline spectra. They extend the well-known Sinc function and generally are the restrictions to the real line of analytic functions in a strip containing the real axis. We investigate various properties of these functions including those related to interpolation, orthogonality, and stability. Moreover, a sampling formula is provided for their construction and some applications for signal analysis are given.

The Fourier transform is undoubtedly one of the most valuable and frequently used tools in signal processing and analysis but it has some limitations. In this paper, we rectify these limitations by proposing a newer version of Fourier transform, namely, Distributed Multiresolution Discrete Fourier Transform (D-MR-DFT) and its application in digital watermarking. The core idea of the proposed watermarking scheme is to decompose an image into four frequency sub-bands using D-MR-DFT and then singular values of every sub-band are modified with the singular values of the watermark. The experimental results show better visual imperceptibility and resiliency of the proposed scheme against intentional or unintentional variety of attacks.

Frames of subspaces for Banach spaces have been introduced and studied. Examples and counter-examples to distinguish various types of frames of subspaces have been given. It has been proved that if a Banach space has a Banach frame, then it also has a frame of subspaces. Also, a necessary and sufficient condition for a sequence of projections, associated with a frame of subspaces, to be unique has been given. Finally, we consider complete frame of subspaces and prove that every weakly compactly generated Banach space has a complete frame of subspaces.

In this paper, we discuss the continuous extension and wavelet approximation of the detected object on a general domain Ω of ℝ². We first extend continuously the image to a square T such that it vanishes on the boundary ∂T. On T∖Ω, the extension has a simple and clear representation which is determined by the equation of the boundary ∂Ω. We expand the extension into wavelet series on ℝ². Since the extension tools are polynomials, by the moment theorem, we know that the sequence of wavelet coefficients obtained by us is sparse. Therefore, we can approximate and analyze the internal information of the object very well even if we only store a few wavelet coefficients.

This paper presents two methods for fusion of infrared (IR) and visible surveillance images. The first method combines Curvelet Transform (CT) with Discrete Wavelet Transform (DWT). As wavelets do not represent long edges well while curvelets are challenged with small features, our objective is to combine both to achieve better performance. The second approach uses Discrete Wavelet Packet Transform (DWPT), which provides multiresolution in high frequency band as well and hence helps in handling edges better. The performance of the proposed methods have been extensively tested for a number of multimodal surveillance images and compared with various existing transform domain fusion methods. Experimental results show that evaluation based on entropy, gradient, contrast etc., the criteria normally used, are not enough, as in some cases, these criteria are not consistent with the visual quality. It also demonstrates that the Petrovic and Xydeas image fusion metric is a more appropriate criterion for fusion of IR and visible images, as in all the tested fused images, visual quality agrees with the Petrovic and Xydeas metric evaluation. The analysis shows that there is significant increase in the quality of fused image, both visually and quantitatively. The major achievement of the proposed fusion methods is its reduced artifacts, one of the most desired feature for fusion used in surveillance applications.

This paper introduces two types of Lorenz-like three-dimensional quadratic autonomous chaotic systems with 7 and 8 new parameters free of choice, respectively. Both systems are investigated at the equilibriums to study their chaotic characteristics. We focus our attention on the second type of the introduced system which consists of three nonlinear quadratic equations. Predictably, coordinates of the equilibriums are prohibitively complex. Therefore, instead of directly analyzing their stability, we prove the asymptotical characterization of equilibriums by utilizing our preliminary results derived for the first type of system. Our result shows that, though the coordinates of equilibriums satisfy a ternary quadratic, the system still contains only three equilibriums in circumstances of chaos. Sufficient conditions for the chaotic appearance of systems are derived. Our results are further verified by numerical simulations and the maximum Lyapunov exponent for several examples. Our research takes a first step in investigating chaos in Lorenz-like dynamic systems with strengthened nonlinearity and general forms of parameters.

A new method for detecting weak linear frequency modulated (LFM) pulse signals buried in additive white Gaussian noise (AWGN) is presented in this paper. The method is based on the features of wavelet transform modulus maxima (WTMM) denoising and auto-correlation filtering theory. Firstly, the frequency-domain information is extracted by auto-correlation matched filtering, and is used to deduce the optimal wavelet decomposition scales. Secondly, let the signal modulus dominate on the biggest scale after the optimal scales decomposition, then keeping the signal modulus and removing the noise modulus at each scale are performed by utilizing the different propagation properties of signal and noise wavelet modulus maxima across the scales. Finally, a reconstructed signal is obtained from the reserved signal modulus with an improved signal-to-noise ratio (SNR), and is used for time-domain information extraction. At the same time, wavelet denoising depends on selecting an optimum wavelet that matches well the shape of the signal. The cross correlation coefficients between signal and db wavelets are calculated and the optimal wavelet to analysis the LFM signal is selected. Simulations show that the method can extract time-frequency information of LFM signal when SNR ≤ -6 dB.

In this paper, a novel feature extraction method called Gabor-based tensor local discriminant embedding (GTLDE) is proposed. GTLDE first gets the high-order statistic information by using a biologically inspired hierarchical model, and then tensor local discriminant embedding (TLDE) is carried out to extract the discriminant features of the image for recognition task. The method we proposed is not only robust to local translation and scale variations, but also has high distinguishing ability. More importantly, our method can achieve high accuracy with a small number of training samples. Experimental results on PolyU-II palmprint database demonstrate the effectiveness of the method we proposed.