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Three-point Nevanlinna-Pick problem in the polydisc

PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY 2015年第4期111卷 887-910页

作者： Kosinski, Lukasz Jagiellonian Univ Fac Math & Comp Sci Inst Math Lojasiewicza 6 PL-30348 Krakow Poland

In the present article, we show that the same property holds for a three-point Pick problem on polydiscs, that is, the solution may be expressed in terms of 3-complex geodesics. Using this idea, we are able to obtain formulas and a uniqueness theorem for solutions of extremal problems. In particular, we determine a class of rational inner functions that solve the interpolation problem. Possible extensions and further investigations are also discussed.

关键词： NEVANLINNA theory PROBLEM solving GEODESICS (Mathematics) UNIQUENESS (Mathematics) interpolation algorithms

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Morphing Linear Features Based on Their Entire Structures

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TRANSACTIONS IN GIS 2015年第5期19卷 653-677页

作者： Deng, Min Peng, Dongliang Cent S Univ Dept Geoinformat Changsha Hunan Peoples R China

In this article, a new morphing method is proposed for two linear features at different scales, based on their entire structures (MLBES in abbreviation). First, the bend structures of the linear features are identified by using a constrained Delaunay triangulation (CDT in abbreviation) model and represented by binary bend-structure trees. By matching the independent bends represented by the bend-structure trees, corresponding independent bends are obtained. These corresponding independent bends are further used to match their child bends based on hierarchical bend structures so that corresponding bends are obtained. On this basis, the two linear features are split into pairs of corresponding subpolylines by the start and end points of the corresponding bends. Second, structures of the corresponding subpolylines are identified by the Douglas-Peucker algorithm and represented by binary line generalization trees (BLG-trees in abbreviation). The corresponding subpolylines are split into smaller corresponding subpolylines by matching the nodes of the BLG-trees. Third, the corresponding points are identified by using the linear interpolation algorithm for every pair of corresponding subpolylines. Finally, straight-line trajectories are employed to generate a family of intermediate-scale linear features. By comparison with other methods, it is found that MLBES is accurate and efficient.

关键词： TRIANGULATION interpolation algorithms TRAJECTORIES (Mechanics) TRANSFORMATIONS (Mathematics) VECTOR data

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Assessment of Similarity of a Set of Impact Response Time Histories

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SAE INTERNATIONAL JOURNAL OF TRANSPORTATION SAFETY 2015年第1期3卷 28-38页

作者： Shi, Yibing Nusholtz, Guy FCA US LLC Auburn Hills MI 48326 USA

Two methods of assessing the similarity of a set of impact test signals have been proposed and used in the literature, which are cumulative variance-based and cross correlation- based. In this study, a normalized formulation unites these two approaches by establishing a relationship between the normalized cumulative variance metric (v), an overall similarity metric, and the normalized magnitude similarity metric (m) and shape similarity metric (s): v=1 - m . s. Each of these ranges between 0 and 1 (for the practical case of signals acquired with the same polarity), and they are independent of the physical unit of measurement. Under generally satisfied conditions, the magnitude similarity m is independent of the relative time shifts among the signals in the set;while the shape similarity s is a function of these. An optimal alignment is defined as the relative shifts corresponding to the minimum of the cumulative variance metric, or equivalently, to the maximum of the shape similarity metric. This system therefore quantifies the similarity of a given set of signals with an "as given" relative time alignment with the following: v = 1- m(p + s(a)), i.e., its overall similarity is partitioned into the shift-invariant normalized magnitude metric m, and the inherent (optimally aligned) normalized shape metric s(a), and a normalized phase metric p which reflects the alignment. An algorithm is provided for automatic search of the optimal shifts for a given set of signals using the cumulative variance as the objective function. The shifts are treated as real numbers instead of integers so that standard continuous variable optimization functions can be used to treat the discrete signals. This is facilitated by an interpolation procedure for shifting a signal with a real-valued time shift. Numerical examples are presented to demonstrate the general effectiveness of the algorithm, and also specific limitations on consistent convergence to the global optimal. Practical measures

关键词： IMPACT response algorithms CRASH testing of automobiles interpolation algorithms INTEGERS MATHEMATICAL optimization

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Accuracy of Sine-wave Frequency Estimation by an Iterative Interpolated DFT Algorithm

Accuracy of Sine-wave Frequency Estimation by an Iterative I...

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32nd Annual IEEE International Instrumentation and Measurement Technology Conference (I2MTC)

作者： Belega, Daniel Petri, Dario Dallet, Dominique Politehn Univ Timisoara Dept Measurements & Opt Elect Timisoara Romania Univ Trento Dept Ind Engn Trento Italy Univ Bordeaux IPB ENSEIRB IMS Lab MATMECA Talence France

ISBN: (纸本)9781479961139

In this paper the accuracy of the sine-wave frequency estimator returned by an iterative Interpolated Discrete Fourier Transform (IpDFT) algorithm based on a Maximum Sidelobe Decay (MSD) window is analyzed. The expressions for the contribution to the frequency estimation error of either the spectral interference from the sine-wave image component and wideband noise are derived. It is shown that two algorithm iterations ensure the minimum noise sensitivity achievable with the adopted window. The accuracy of the derived expressions is verified by means of computer simulations and validated by experimental results.

关键词： Uncertainty analysis frequency estimation interpolation algorithms sine-wave windowing

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A Block-Based Regularized Approach for Image interpolation

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MATHEMATICAL PROBLEMS IN ENGINEERING 2014年第1期2014卷 1-8页

作者： Chen, Li Huang, Xiaotong Tian, Jing Wuhan Univ Sci & Technol Sch Comp Sci & Technol Wuhan 430081 Peoples R China Wuhan Univ Sci & Technol Hubei Prov Key Lab Intelligent Informat Proc & Re Wuhan 430081 Peoples R China

This paper presents a new efficient algorithm for image interpolation based on regularization theory. To render a high-resolution (HR) image from a low-resolution (LR) image, classical interpolation techniques estimate the missing pixels from the surrounding pixels based on a pixel-by-pixel basis. In contrast, the proposed approach formulates the interpolation problem into the optimization of a cost function. The proposed cost function consists of a data fidelity term and regularization functional. The closed-form solution to the optimization problem is derived using the framework of constrained least squares minimization, by incorporating Kronecker product and singular value decomposition (SVD) to reduce the computational cost of the algorithm. The effect of regularization on the interpolation results is analyzed, and an adaptive strategy is proposed for selecting the regularization parameter. Experimental results show that the proposed approach is able to reconstruct high-fidelity HR images, while suppressing artifacts such as edge distortion and blurring, to produce superior interpolation results to that of conventional image interpolation techniques.

关键词： interpolation algorithms IMAGE analysis REGULARIZATION (Mathematics) HIGH resolution imaging PIXELS MATHEMATICAL optimization

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Sample Data Synchronization and Harmonic Analysis Algorithm Based on Radial Basis Function interpolation

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MATHEMATICAL PROBLEMS IN ENGINEERING 2014年第1期2014卷 1-7页

作者： Zhang, Huaiqing Chen, Yu Fu, Zhihong Liu, Ran Chongqing Univ State Key Lab Transmiss Equipment & Syst Safety & Chongqing 400044 Peoples R China

The spectral leakage has a harmful effect on the accuracy of harmonic analysis for asynchronous sampling. This paper proposed a time quasi-synchronous sampling algorithm which is based on radial basis function (RBF) interpolation. Firstly, a fundamental period is evaluated by a zero-crossing technique with fourth-order Newton's interpolation, and then, the sampling sequence is reproduced by the RBF interpolation. Finally, the harmonic parameters can be calculated by FFT on the synchronization of sampling data. Simulation results showed that the proposed algorithm has high accuracy in measuring distorted and noisy signals. Compared to the local approximation schemes as linear, quadric, and fourth-order Newton interpolations, the RBF is a global approximation method which can acquire more accurate results while the time-consuming is about the same as Newton's.

关键词： RADIAL basis functions interpolation algorithms HARMONIC analysis (Mathematics) SYNCHRONIZATION APPROXIMATION theory MATHEMATICAL analysis

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Post-processing of interpolation-based super-resolution mapping with morphological filtering and fraction refilling

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INTERNATIONAL JOURNAL OF REMOTE SENSING 2014年第13期35卷 5251-5262页

作者： Ling, Feng Fang, Shiming Li, Wenbo Li, Xiaodong Xiao, Fei Zhang, Yihang Du, Yun Chinese Acad Sci Inst Geodesy & Geophys Key Lab Environm & Disaster Monitoring & Evaluat Wuhan Hubei Peoples R China China Univ Geosci Sch Publ Adm Wuhan 430074 Peoples R China Chinese Acad Sci Inst Intelligent Machines Hefei Peoples R China

interpolation-based super-resolution mapping (SRM) is a popular model to produce a super-resolution land-cover map from coarse-resolution fraction images. This model can maintain the holistic land-cover features;however, it also results in a super-resolution land-cover map that includes many speckle and linear artefacts, due to errors caused by both the interpolation and the label assignment steps. In this article, we propose a novel two-step post-processing algorithm for interpolation-based SRM. The first step is morphological filtering, which is used to eliminate artefacts and to preserve land-cover features in the super-resolution land-cover map produced by interpolation-based SRM. The second step is fraction refilling, which is applied to make the fraction constraints satisfied and the super-resolution land-cover map locally smooth. Based on the application to three simulated images with various interpolation algorithms and morphological filter operations, the performance of the proposed post-processing algorithm was assessed. The results show that the proposed post-processing algorithm increases the accuracy of the super-resolution land-cover map and is suitable for different interpolation-based SRM models.

关键词： HIGH resolution imaging LAND cover REMOTE sensing interpolation algorithms IMAGE processing

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The Improved Kriging interpolation Algorithm for Local Underwater Terrain Based on Fractal Compensation

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MATHEMATICAL PROBLEMS IN ENGINEERING 2014年第1期2014卷 1-8页

作者： Chen, Pengyun Li, Ye Su, Yumin Chen, Xiaolong Harbin Engn Univ Sci & Technol Underwater Vehicle Lab Harbin 150001 Peoples R China China Ship Dev & Design Ctr Wuhan 430064 Peoples R China

The interpolation-reconstruction of local underwater terrain using the underwater digital terrain map (UDTM) is an important step for building an underwater terrain matching unit and directly affects the accuracy of underwater terrain matching navigation. The Kriging method is often used in terrain interpolation, but, with this method, the local terrain features are often lost. Therefore, the accuracy cannot meet the requirements of practical application. Analysis of the geographical features is performed on the basis of the randomness and self-similarity of underwater terrain. We extract the fractal features of local underwater terrain with the fractal Brownian motion model, compensating for the possible errors of the Kriging method with fractal theory. We then put forward an improved Kriging interpolation method based on this fractal compensation. interpolation-reconstruction tests show that the method can simulate the real underwater terrain features well and that it has good usability.

关键词： KRIGING interpolation algorithms FRACTAL analysis BROWNIAN motion processes MATCHING theory

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An efficient dichotomizing interpolation algorithm for the refinement of TIN-based terrain surface from contour maps

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COMPUTERS & GEOSCIENCES 2014年第0期72卷 105-121页

作者： Li, Lin Kuai, Xi Wuhan Univ Sch Resource & Environm Sci Wuhan 430079 Peoples R China

Generating a triangulated irregular network (TIN) from contour maps is the most commonly used approach to build Digital Elevation Models (DEMs) for geo-databases. A well-known problem when building a TIN is that many pan slope triangles (or PSTs) may emerge from the vertices of contour lines. Those triangles should be eliminated from the TIN by adding additional terrain points when refining the local TIN. There are many methods and algorithms available for eliminating PSTs in a TIN, but their performances may not satisfy the requirements of some applications where efficiency rather than completeness is critical. This paper investigates commonly-used processes for eliminating PSTs and puts forward a new algorithm, referred to as 'dichotomizing' interpolation algorithm, to achieve a higher efficiency than from the conventional 'skeleton' extraction algorithm. Its better performance comes from reducing the number of the additional interpolated points to only those that are sufficient and necessary for eliminating PSTs. This goal is reached by dichotomizing PST polygons iteratively and locating additional points in the geometric centers of the polygons. This study verifies, both theoretically and experimentally, the higher efficiency of this new dichotomizing algorithm and also demonstrates its reliability for building DEMs in terms of accuracy for estimating terrain surface elevation. (C) 2014 Elsevier Ltd. All rights reserved.

关键词： TIN Digital elevation models (DEMs) Contour maps Terrain surface modeling interpolation algorithms

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Nonlinear model reduction for dynamical systems using sparse sensor locations from learned libraries

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Physical Review E 2015年第3期92卷 033304-033304页

作者： Syuzanna Sargsyan Steven L. Brunton J. Nathan Kutz Department of Applied Mathematics University of Washington Seattle Washington 98195-3925 USA Department of Mechanical Engineering University of Washington Seattle Washington 98195 USA

We demonstrate the synthesis of sparse sampling and dimensionality reduction to characterize and model nonlinear dynamical systems over a range of bifurcation parameters. First, we construct modal libraries using the classical proper orthogonal decomposition in order to expose the dominant low-rank coherent structures. Here, libraries of the nonlinear terms are also constructed in order to take advantage of the discrete empirical interpolation method and projection that allows for the approximation of nonlinear terms from a sparse number of grid points. The selected grid points are shown to be effective sensing and measurement locations for characterizing the underlying dynamics, stability, and bifurcations of nonlinear dynamical systems. The use of empirical interpolation points and sparse representation facilitates a family of local reduced-order models for each physical regime, rather than a higher-order global model, which has the benefit of physical interpretability of energy transfer between coherent structures. The method advocated also allows for orders-of-magnitude improvement in computational speed and memory requirements. To illustrate the method, the discrete interpolation points and nonlinear modal libraries are used for sparse representation in order to classify and reconstruct the dynamic bifurcation regimes in the complex Ginzburg-Landau equation. It is also shown that point measurements of the nonlinearity are more effective than linear measurements when sensor noise is present.

关键词： Nonlinear dynamical systems Compressed sensing (Signal processing) Energy transfer Bifurcation theory interpolation algorithms Landau theory

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