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Xiaobo Qu - One of the best experts on this subject based on the ideXlab platform.

  • vandermonde factorization of hankel matrix for Complex Exponential signal recovery application in fast nmr spectroscopy
    IEEE Transactions on Signal Processing, 2018
    Co-Authors: Jiaxi Ying, Gongguo Tang, Zhong Chen, Xiaobo Qu
    Abstract:

    Many signals are modeled as a superposition of Exponential functions in spectroscopy of chemistry, biology, and medical imaging. This paper studies the problem of recovering Exponential signals from a random subset of samples. We exploit the Vandermonde structure of the Hankel matrix formed by the Exponential signal and formulate signal recovery as Hankel matrix completion with Vandermonde factorization (HVaF). A numerical algorithm is developed to solve the proposed model and its sequence convergence is analyzed theoretically. Experiments on synthetic data demonstrate that HVaF succeeds over a wider regime than the state-of-the-art nuclear-norm-minimization-based Hankel matrix completion method, while it has a less restriction on frequency separation than the state-of-the-art atomic norm minimization and fast iterative hard thresholding methods. The effectiveness of HVaF is further validated on biological magnetic resonance spectroscopy data.

  • robust recovery of Complex Exponential signals from random gaussian projections via low rank hankel matrix reconstruction
    Applied and Computational Harmonic Analysis, 2016
    Co-Authors: Xiaobo Qu, Weiyu Xu, Guibo Ye
    Abstract:

    Abstract This paper explores robust recovery of a superposition of R distinct Complex Exponential functions with or without damping factors from a few random Gaussian projections. We assume that the signal of interest is of 2 N − 1 dimensions and R 2 N − 1 . This framework covers a large class of signals arising from real applications in biology, automation, imaging science, etc. To reconstruct such a signal, our algorithm is to seek a low-rank Hankel matrix of the signal by minimizing its nuclear norm subject to the consistency on the sampled data. Our theoretical results show that a robust recovery is possible as long as the number of projections exceeds O ( R ln 2 ⁡ N ) . No incoherence or separation condition is required in our proof. Our method can be applied to spectral compressed sensing where the signal of interest is a superposition of R Complex sinusoids. Compared to existing results, our result here does not need any separation condition on the frequencies, while achieving better or comparable bounds on the number of measurements. Furthermore, our method provides theoretical guidance on how many samples are required in the state-of-the-art non-uniform sampling in NMR spectroscopy. The performance of our algorithm is further demonstrated by numerical experiments.

Xingyuan Wang - One of the best experts on this subject based on the ideXlab platform.

  • robust zero watermarking algorithm based on polar Complex Exponential transform and logistic mapping
    Multimedia Tools and Applications, 2017
    Co-Authors: Chunpeng Wang, Xingyuan Wang, Xingjun Chen, Chuan Zhang
    Abstract:

    This paper introduces a new zero-watermarking algorithm based on polar Complex Exponential transform (PCET) and logistic mapping. This algorithm takes advantage of the geometric invariance of PCET to improve the robustness of the algorithm against geometric attacks, and the logistic mapping’s sensitivity to initial values to improve the security of the algorithm. First, the algorithm computes the PCET of the original grayscale image. Then it randomly selects PCET coefficients based on logistic mapping, and computes their magnitudes to obtain a binary feature image. Finally, it performs an exclusive-or operation between the binary feature image and the scrambled logo image to obtain the zero-watermark image. At the stage of copyright verification, the image copyright can be determined by performing the exclusive-or operation between the feature image and the verification image and comparing the resulting image to the original logo image. Experimental results show that this algorithm has excellent robustness against geometric attacks and common image processing attacks and better performance compared to other zero-watermarking algorithms.

  • julia sets of newton s method for a class of Complex Exponential function f z p z eq z
    Nonlinear Dynamics, 2010
    Co-Authors: Xingyuan Wang, Yuanyuan Sun, Jun-mei Song
    Abstract:

    In this paper, we analyze the theory of the Julia set (J set) of Newton’s method, construct the Julia sets of Newton’s method of function $F(z)=ze^{z^{w}}$ (w∈ℂ) through iteration method, and analyze the attracting region of the two fixed points 0 and ∞ when w are different values. Consequently, we draw the following conclusions: (1) When the judge conditions for the iterative algorithm are changed to |N(z n )−z n |≤EOF, the properties of the figures in our experiments are contrary to the conclusions in (Wegner and Peterson, Fractal Creations, pp. 168–231, 1991); (2) The attracting regions of the fixed points 0 and ∞ for w=2n (n=0,±2,±4,…) are symmetrical about x-axis and y-axis; select the main argument to be in [−π,π), for arbitrary w=α (α∈ℂ), the attracting regions of the fixed points 0 and ∞ are symmetrical about the x-axis; (3) The attracting regions of the two fixed points 0 and ∞ of J set for w=±η have rotational symmetry of η times; (4) If w=−4.7, k=0.8, then the attracting regions of different magnifications display a startling similarity, J set holds infinite self-similar structures; (5) When w is a Complex number, because the selection of main argument θ z in the negative x-axis is not continuous, the fault and rupture of the attracting regions of the two fixed points 0 and ∞ appear only in the negative x-axis.

  • julia set of the newton transformation for solving some Complex Exponential equation
    Fractals, 2009
    Co-Authors: Xingyuan Wang, Xuejing Yu
    Abstract:

    We extend Kim's Complex Exponential function, come up with theory about the Julia set of Newton's transformation for general Exponential equation, analyze the behavior of the roots of some Complex Exponential equation, and prove the symmetry, boundedness and embedding topology distribution structure of basins of attraction of the Julia set in theory.

Jitendra K. Tugnait - One of the best experts on this subject based on the ideXlab platform.

  • Doubly Selective Channel Estimation Using Exponential Basis Models and Subblock Tracking
    IEEE Transactions on Signal Processing, 2010
    Co-Authors: Jitendra K. Tugnait, Shuangchi He
    Abstract:

    Three versions of a novel adaptive channel estimation approach, exploiting the over-sampled Complex Exponential basis expansion model (CE-BEM), is presented for doubly selective channels, where we track the BEM coefficients rather than the channel tap gains. Since the time-varying nature of the channel is well captured in the CE-BEM by the known Exponential basis functions, the time variations of the (unknown) BEM coefficients are likely much slower than those of the channel, and thus more convenient to track. We propose a ¿subblockwise¿ tracking scheme for the BEM coefficients using time-multiplexed (TM) periodically transmitted training symbols. Three adaptive algorithms, including a Kalman filtering scheme based on an assumed autoregressive (AR) model of the BEM coefficients, and two recursive least-squares (RLS) schemes not requiring any model for the BEM coefficients, are investigated for BEM coefficient tracking. Simulation examples illustrate the superior performance of our approach over several existing doubly selective channel estimators.

  • Turbo equalization for doubly-selective fading channels using nonlinear kalman filtering and basis expansion models
    IEEE Transactions on Wireless Communications, 2010
    Co-Authors: Jitendra K. Tugnait
    Abstract:

    We present a turbo (iterative) equalization receiver with fixed-lag nonlinear Kalman filtering for coded data transmission over doubly-selective channels. The proposed receiver exploits the Complex Exponential basis expansion model (CEBEM) for the overall channel variations, and an autoregressive (AR) model for the BEM coefficients. We extend an existing turbo equalization approach based on symbol-wise AR modeling of channels to channels based on BEM's. In the receiver an adaptive equalizer using nonlinear Kalman filters with delay is coupled with a soft-input soft-output (SISO) decoder to iteratively perform equalization and decoding. The adaptive equalizer jointly optimizes the estimates of the BEM coefficients and data symbols, thereby automatically accounting for correlation between data symbols and channel tap gains. An extrinsic information transfer (EXIT) chart analysis of the proposed approach is also presented. Simulation examples demonstrate that our CE-BEM-based approach significantly outperforms the existing symbol-wise AR model-based turbo equalizer.

Pramod Rastogi - One of the best experts on this subject based on the ideXlab platform.

  • strain curvature and twist measurements in digital holographic interferometry using pseudo wigner ville distribution based method
    Review of Scientific Instruments, 2009
    Co-Authors: Gannavarpu Rajshekhar, Sai Siva Gorthi, Pramod Rastogi
    Abstract:

    Measurement of strain, curvature, and twist of a deformed object play an important role in deformation analysis. Strain depends on the first order displacement derivative, whereas curvature and twist are determined by second order displacement derivatives. This paper proposes a pseudo-Wigner-Ville distribution based method for measurement of strain, curvature, and twist in digital holographic interferometry where the object deformation or displacement is encoded as interference phase. In the proposed method, the phase derivative is estimated by peak detection of pseudo-Wigner-Ville distribution evaluated along each row/column of the reconstructed interference field. A Complex Exponential signal with unit amplitude and the phase derivative estimate as the argument is then generated and the pseudo-Wigner-Ville distribution along each row/column of this signal is evaluated. The curvature is estimated by using peak tracking strategy for the new distribution. For estimation of twist, the pseudo-Wigner-Ville distribution is evaluated along each column/row (i.e., in alternate direction with respect to the previous one) for the generated Complex Exponential signal and the corresponding peak detection gives the twist estimate.

  • strain curvature and twist measurements in digital holographic interferometry using pseudo wigner ville distribution based method
    Review of Scientific Instruments, 2009
    Co-Authors: Gannavarpu Rajshekhar, Sai Siva Gorthi, Pramod Rastogi
    Abstract:

    Measurement of strain, curvature, and twist of a deformed object play an important role in deformation analysis. Strain depends on the first order displacement derivative, whereas curvature and twist are determined by second order displacement derivatives. This paper proposes a pseudo-Wigner–Ville distribution based method for measurement of strain, curvature, and twist in digital holographic interferometry where the object deformation or displacement is encoded as interference phase. In the proposed method, the phase derivative is estimated by peak detection of pseudo-Wigner–Ville distribution evaluated along each row/column of the reconstructed interference field. A Complex Exponential signal with unit amplitude and the phase derivative estimate as the argument is then generated and the pseudo-Wigner–Ville distribution along each row/column of this signal is evaluated. The curvature is estimated by using peak tracking strategy for the new distribution. For estimation of twist, the pseudo-Wigner–Ville di...

Xiangyang Wang - One of the best experts on this subject based on the ideXlab platform.

  • color image zero watermarking based on fast quaternion generic polar Complex Exponential transform
    Signal Processing-image Communication, 2020
    Co-Authors: Hongying Yang, Panpan Niu, Xiangyang Wang
    Abstract:

    Abstract As one promising solution, zero-watermarking techniques have been proposed to enhance the image visual quality and applied to protect the intellectual property rights of the medical images, remote sensing images and military images. Owing to their favorable image description capability and geometric invariance, moments and moment invariants have become a popular tool for the zero-watermarking. However, two issues of the moments-based zero-watermarking methods should be addressed: First, most of them ignore the analysis and experiment on discriminability, resulting in a high false positive ratio; Second, direct computation of the moments from their definition is inefficient, numerically unstable and inaccurate, which severely affects the performances of these moments-based methods. To overcome the two challenges, in this paper, we present a Fast Quaternion Generic Polar Complex Exponential Transform (FQGPCET) based color image zero-watermarking algorithm. We first propose a novel computation strategy, i.e. FGPCET, to solve the moments computing problems. We then show that it is possible to generate a robust and discriminative image feature, by mixing the low-order QGPCET moments/coefficients. And finally, we develop a new color image zero-watermarking approach using FQGPCET and asymmetric tent map. Theoretical analysis and experimental results show that the proposed zero-watermarking algorithm achieves a good trade-off between robustness and discriminability, and has certain superiority in terms of security, capacity and time Complexity.

  • quaternion polar Complex Exponential transform for invariant color image description
    Applied Mathematics and Computation, 2015
    Co-Authors: Xiangyang Wang, Hongying Yang, Pei Wang
    Abstract:

    Moments and moment invariants have been widely used as a basic feature descriptors in image analysis, pattern recognition, and image retrieval. However, they are mainly used to deal with the binary or gray-scale images, which lose some significant color information. Recently, quaternion techniques were introduced to conventional image moments (including Fourier-Mellin moments, Zernike/Pseudo Zernike moments, and Bessel-Fourier moments, etc.) for describing color images, and some quaternion moment and moment invariants were developed. But, the conventional image moments usually cannot effectively capture the image information, especially the edges. Besides, the kernel computation of them involves computation of a number of factorial terms, which inevitably cause the numerical stability of these moments. Based on effective polar Complex Exponential transform (PCET) and algebra of quaternions, we introduced the quaternion polar Complex Exponential transform (QPCET) for describing color images in this paper, which can be seen as the generalization of PCET for gray-level images. It is shown that the QPCETs can be obtained from the PCET of each color channel. We derived and analyzed the rotation, scaling, and translation (RST) invariant property of QPCET. We also discussed the problem of color image retrieval using QPCET. Experimental results are provided to illustrate the efficiency of the proposed color image descriptors.