The Experts below are selected from a list of 156 Experts worldwide ranked by ideXlab platform
Ting-zhu Huang - One of the best experts on this subject based on the ideXlab platform.
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Laplace Function based nonconvex surrogate for low-rank tensor completion
Signal Processing: Image Communication, 2019Co-Authors: Xi-le Zhao, Jia-qing Miao, Si Wang, Ting-zhu HuangAbstract:Abstract Recently, the tensor nuclear norm (TNN), which is the convex surrogate for tensor multi rank, has been successfully applied to the low-rank tensor completion (LRTC) problem. However, treating each singular value equally restricts the capability of TNN. In this work, we suggest the Laplace Function based surrogate for tensor multi rank, which adaptively assigns weights to different singular values. We propose the corresponding surrogate based LRTC model and develop an efficient alternating direction method of multipliers (ADMM) to tackle the proposed model. Extensive experiments demonstrate that the proposed method outperforms state-of-the-art methods both quantitatively and qualitatively.
Almerico Murli - One of the best experts on this subject based on the ideXlab platform.
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A smoothing spline that approximates Laplace transform Functions only known on measurements on the real axis
Inverse Problems, 2012Co-Authors: Luisa D'amore, Ardelio Galletti, Rosanna Campagna, Livia Marcellino, Almerico MurliAbstract:The scientific and application-oriented interest in the Laplace transform and its inversion is testified by more than 1000 publications in the last century. Most of the inversion algorithms available in the literature assume that the Laplace transform Function is available everywhere. Unfortunately, such an assumption is not fulfilled in the applications of the Laplace transform. Very often, one only has a finite set of data and one wants to recover an estimate of the inverse Laplace Function from that. We propose a fitting model of data. More precisely, given a finite set of measurements on the real axis, arising from an unknown Laplace transform Function, we construct a dth degree generalized polynomial smoothing spline, where d = 2m − 1, such that internally to the data interval it is a dth degree polynomial complete smoothing spline minimizing a regularization Functional, and outside the data interval, it mimics the Laplace transform asymptotic behavior, i.e. it is a rational or an exponential Function (the end behavior model), and at the boundaries of the data set it joins with regularity up to order m − 1, with the end behavior model. We analyze in detail the generalized polynomial smoothing spline of degree d = 3. This choice was motivated by the (ill)conditioning of the numerical computation which strongly depends on the degree of the complete spline. We prove existence and uniqueness of this spline. We derive the approximation error and give a priori and computable bounds of it on the whole real axis. In such a way, the generalized polynomial smoothing spline may be used in any real inversion algorithm to compute an approximation of the inverse Laplace Function. Experimental results concerning Laplace transform approximation, numerical inversion of the generalized polynomial smoothing spline and comparisons with the exponential smoothing spline conclude the work.
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A Modification of Weeks’ Method for Numerical Inversion of the Laplace Transform in the Real Case Based on Automatic Differentiation
Advances in Automatic Differentiation, 2008Co-Authors: Salvatore Cuomo, Luisa D'amore, Mariarosaria Rizzardi, Almerico MurliAbstract:Numerical inversion of the Laplace transform on the real axis is an inverse and ill-posed problem. We describe a powerful modification of Weeks’ Method, based on automatic differentiation, to be used in the real inversion. We show that the automatic differentiation technique assures accurate and efficient numerical computation of the inverse Laplace Function.
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numerical regularization of a real inversion formula based on the Laplace transform s eigenFunction expansion of the inverse Function
Inverse Problems, 2007Co-Authors: Almerico Murli, Salvatore Cuomo, Luisa Damore, Ardelio GallettiAbstract:We describe the numerical approximation of the inverse Laplace Function based on the Laplace transform's eigenFunction expansion of the inverse Function, in a real case. The error analysis allows us to introduce a regularization technique involving computable upper bounds of amplification factors of local errors introduced by the computational process. A regularized solution is defined as one which is obtained within the maximum attainable accuracy. Moreover the regularization parameter, that in this case coincides with the truncation parameter of the eigenFunction expansion, is dynamically computed by the algorithm itself in such a way that it provides the minimum of the global error bound.
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Real inversion of a Laplace transform
Experimental and Numerical Methods for Solving Ill-Posed Inverse Problems: Medical and Nonmedical Applications, 1995Co-Authors: Luisa D'amore, Almerico MurliAbstract:This paper is concerned with the real invserion of a Laplace tranform Function F(s) equals L[f(t)]. The real inversion problem is that of reconstructing f(t) from known values of F(s), given only at real points. Numerical inversion of a Laplace transform is a very difficult problem to be solved in general, as shown in the survey written by Davies and Martin in 1979. Actually, this is still true. It is well known that the numerical solution of the real inversion problem is much more difficult than that of the complex one. Briefly, this is due to an intrinsic ill-posedness of the real inversion problem in the sense that small changes in data can cause arbitrary large changes in the solutionl. This is reflected in ill-conditioning of the discrete model. We propose a numerical method for the real inversion problem based on a Fourier series expansion of f(t). Introducing some kind of regularization we show how it is possible to approximate the Fourier coefficients of f(t), and then to compute the inverse Laplace Function, only using the knowledge of the restriction of F(s) on the real axes.© (1995) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.
Xi-le Zhao - One of the best experts on this subject based on the ideXlab platform.
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Laplace Function based nonconvex surrogate for low-rank tensor completion
Signal Processing: Image Communication, 2019Co-Authors: Xi-le Zhao, Jia-qing Miao, Si Wang, Ting-zhu HuangAbstract:Abstract Recently, the tensor nuclear norm (TNN), which is the convex surrogate for tensor multi rank, has been successfully applied to the low-rank tensor completion (LRTC) problem. However, treating each singular value equally restricts the capability of TNN. In this work, we suggest the Laplace Function based surrogate for tensor multi rank, which adaptively assigns weights to different singular values. We propose the corresponding surrogate based LRTC model and develop an efficient alternating direction method of multipliers (ADMM) to tackle the proposed model. Extensive experiments demonstrate that the proposed method outperforms state-of-the-art methods both quantitatively and qualitatively.
E. G. Bezrukova - One of the best experts on this subject based on the ideXlab platform.
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analytical representation of the surface wave generated by an antenna at the interface between two homogeneous media
Physics of Wave Phenomena, 2010Co-Authors: E A Rudenchik, L. B. Volkomirskaya, A. E. Reznikov, E. G. BezrukovaAbstract:Theoretical approach to the solution of georadiolocation (inverse) problem of reconstructing the antenna current and the permittivity of the underlying surface, based on the measurements of the field propagating along the Earth℉s surface, is proposed. An expression for the tangential component of the electric field of the surface wave from a transmitting antenna lying in the plane of discontinuity of two homogeneous media is expressed in terms of the Laplace Function Ŵ(q, ζ) of two complex arguments for any discontinuity parameters. The Function Ŵ(q, ζ) is presented as series, which make it possible to calculate rapidly the values of Ŵ(q, ζ) and investigate its analytic properties. The inverse Laplace transform is performed by integrating the Function Ŵ(q, ζ) over closed contours. The corresponding integrals are proper in this case, due to which the calculation time greatly decreases in comparison with the Fourier transform. When the permittivity dispersion can be neglected, the tangential component of the surface wave is algebraically expressed in terms of the Function Ŵ(q, ζ). This circumstance allows one to decrease the time for calculating the surface wave at a specified point to several milliseconds and determine both the current through the transmitting antenna and the permittivity of the underlying surface for a few seconds.
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Presentation of the field surface wave generated by an antenna at the interface of two homogeneous media
2010 5th International Confernce on Ultrawideband and Ultrashort Impulse Signals, 2010Co-Authors: A. E. Rudenchik, L. B. Volkomirskaya, A. E. Reznikov, E. G. BezrukovaAbstract:In circumstances where the dispersion of the permittivity can be neglected, the tangential component of the surface wave is expressed through the Laplace Function of two complex arguments algebraically. This reduces the computation time of the surface wave at a given point to a few milliseconds, and to determine the current in the radiating antenna, as well as the dielectric constant of the underlying surface, for the time of the order of several seconds. Obtain estimates of the surface wave field for the most typical parameters of soils. These calculations can be used to select regularizators inverse GPR for quantitative calculations of the parameters of the soil and for the qualitative interpretation of GPR data.
Zhenming Peng - One of the best experts on this subject based on the ideXlab platform.
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Infrared Small Target Detection via Non-Convex Tensor Rank Surrogate Joint Local Contrast Energy
Remote Sensing, 2020Co-Authors: Xuewei Guan, Landan Zhang, Suqi Huang, Zhenming PengAbstract:Small target detection is a crucial technique that restricts the performance of many infrared imaging systems. In this paper, a novel detection model of infrared small target via non-convex tensor rank surrogate joint local contrast energy (NTRS) is proposed. To improve the latest infrared patch-tensor (IPT) model, a non-convex tensor rank surrogate merging tensor nuclear norm (TNN) and the Laplace Function, is utilized for low rank background patch-tensor constraint, which has a useful property of adaptively allocating weight for every singular value and can better approximate l 0 -norm. Considering that the local prior map can be equivalent to the saliency map, we introduce a local contrast energy feature into IPT detection framework to weight target tensor, which can efficiently suppress the background and preserve the target simultaneously. Besides, to remove the structured edges more thoroughly, we suggest an additional structured sparse regularization term using the l 1 , 1 , 2 -norm of third-order tensor. To solve the proposed model, a high-efficiency optimization way based on alternating direction method of multipliers with the fast computing of tensor singular value decomposition is designed. Finally, an adaptive threshold is utilized to extract real targets of the reconstructed target image. A series of experimental results show that the proposed method has robust detection performance and outperforms the other advanced methods.
