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A Block-Based Regularized Approach for Image interpolation

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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Smart averaging interpolation algorithm comparative test

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GEOPHYSICAL PROSPECTING 2016年第3期64卷 642-656页

作者： Krilov, D. Vaniarho, Ya Basaev, D. LLC Gazprom VNIIGAZ Sci Ctr Gaz Resources Razvilk Moscow 142717 Moscow Region Russia CJSC ROSPAN INTERNATIONAL Moscow Russia

In many practical cases, it is necessary to characterize the explored area with a regular set of geodata. Regular matrix data (e.g., ordinary maps) are calculated via existing data interpolation and extrapolation. For low frequency (oversampled) data acquired within a dense profile net (e.g., seismic three-dimensional structural or gravity mapping), this procedure is mathematically more or less stable and, to a certain extent, unique since we might neglect discrepancies resulting from different interpolations. The situation is quite different for high-resolution and high-frequency contaminated data (e.g., raw seismic attributes or geochemistry measurements) represented by sparse profiling. Considering the variety of exploration cases, the investigation of different interpolation algorithm efficiency seems very important. Since it is impossible to compare all algorithms by means of formal mathematics, we have designed a test program. A representative set of seismic attribute maps has been artificially destroyed by introducing blank values (from 20% up to 95%) and then restored by different interpolation algorithms bicubic, bilinear, nearest neighbor, and smart averaging. Smart averaging interpolation is done in a live window. The position, form, and size of the window are determined by some mathematical criterion on a trial-and-error basis. Discrepancies between restored and initial (true) data have been assessed and analysed. It is shown that the total (absolute) efficiency and comparative (relative) efficiency of the algorithms depend mostly upon the initial interpolant data characteristics. Identifying the best interpolation algorithm for all interpretive cases seems impossible. Some aspects of data processing are discussed in connection with interpolation accuracy.

关键词： interpolation algorithms GEODATABASES GEOCHEMISTRY SEISMOLOGY EXTRAPOLATION

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interpolation by Cauchy-Vandermonde systems and applications

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2000年第1-2期122卷 203-222页

作者： Mühlbach, G Univ Hannover Inst Angew Math D-30060 Hannover Germany

Cauchy-Vandermonde systems consist of rational functions with prescribed poles. They are complex ECT-systems allowing Hermite interpolation for any dimension of the basic spate. A survey of interpolation procedures using CV-systems is given, some equipped with short new proofs, which generalize the well-known formulas of Lagrange, Neville-Aitken and Newton for interpolation by algebraic polynomials. The arithmetical complexitiy is O(N-2) for N Hermits data. Also, inversion formulas for the Cauchy-Vandermonde matrix are surveyed. Moreover, a new algorithm solving the system of N linear Cauchy-Vandermonde equations for multiple nodes and multiple poles recursively is given which does not require additional partial fraction decompositions. As an application construction of rational B-splines with prescribed poles is discussed. (C) 2000 Elsevier Science B.V. All rights reserved. MSC: 41A05;65D05.

关键词： prescribed poles Cauchy-Vandermonde systems interpolation algorithms

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Fast rational interpolation, Reed-Solomon decoding, and the linear complexity profiles of sequences

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IEEE TRANSACTIONS ON INFORMATION THEORY 1997年第2期43卷 537-548页

作者： Blackburn, SR Department of Mathematics University of London Egham Surrey UK

An asymptotically fast algorithm for solving the generalized rational interpolation problem is presented, This problem has been studied as part of system theory and is related to the solution of the classical and Welch-Berlekamp key equations which arise in Reed-Solomon decoding, The algorithm can also be used to compute the linear complexity profile of a binary sequence of length m using only O(m(log m)(2) log log m) bit operations.

关键词： key equations Reed-Solomon decoding linear complexity profiles interpolation algorithms

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Guiding Craig interpolation with domain-specific abstractions

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ACTA INFORMATICA 2016年第4期53卷 387-424页

作者： Leroux, Jerome Rummer, Philipp Subotic, Pavle Univ Bordeaux 351 Cours Liberat Talence France Uppsala Univ Box 337 S-75105 Uppsala Sweden

Craig interpolation is a standard method to construct and refine abstractions in model checking. To obtain abstractions that are suitable for the verification of software programs or hardware designs, model checkers rely on theorem provers to find the right interpolants, or interpolants containing the right predicates, in a generally infinite lattice of interpolants for any given interpolation problem. We present a semantic and solver-independent framework for systematically exploring interpolant lattices, based on the notion of interpolation abstraction. We discuss how interpolation abstractions can be constructed for a variety of logics, and how they can be applied in the context of software model checking.

关键词： interpolation algorithms DOMAIN specificity LATTICE theory ABSTRACT thought PREDICATE (Logic)

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Scattered and track data interpolation using an efficient strip searching procedure

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APPLIED MATHEMATICS AND COMPUTATION 2011年第12期217卷 5949-5966页

作者： Allasia, G. Besenghi, R. Cavoretto, R. De Rossi, A. Univ Turin Dept Math I-10123 Turin Italy

A new local algorithm for bivariate interpolation of large sets of scattered and track data is presented. The method, which changes partially depending on the kind of data, is based on the partition of the interpolation domain in a suitable number of parallel strips, and, starting from these, on the construction for any data point of a square neighbourhood containing a convenient number of data points. Then, the well-known modified Shepard's formula for surface interpolation is applied with some effective improvements. The proposed algorithm is very fast, owing to the optimal nearest neighbour searching, and achieves good accuracy. Computational cost and storage requirements are analyzed. Moreover, the efficiency and reliability of the algorithm are shown by several numerical tests, also performed by Renka's algorithm for a comparison. (C) 2010 Elsevier Inc. All rights reserved.

关键词： Continuous surface modelling interpolation algorithms Radial basis functions Scattered and track data Shepard's formulas

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Three-Dimensional Short-Term Prediction Model of Dissolved Oxygen Content Based on PSO-BPANN Algorithm Coupled with Kriging interpolation

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MATHEMATICAL PROBLEMS IN ENGINEERING 2016年第1期2016卷 1-10页

作者： Chen, Yingyi Xu, Jing Yu, Huihui Zhen, Zhumi Li, Daoliang China Agr Univ Coll Elect & Informat Engn Beijing 100083 Peoples R China Minist Agr Key Lab Agr Informat Acquisit Technol Beijing 100083 Peoples R China Beijing Engn & Technol Res Ctr Internet Things Ag Beijing 100083 Peoples R China

Dissolved oxygen (DO) content is a significant aspect of water quality in aquaculture. Prediction of dissolved oxygen may timely avoid the financial loss caused by inappropriate dissolved oxygen content and three-dimensional prediction can achieve more accurate and overall guidance. Therefore, this study presents a three-dimensional short-term prediction model of dissolved oxygen in crab aquaculture ponds based on back propagation artificial neural network (BPANN) optimized by particle swarm optimization (PSO), which coupled with Kriging method. In this model, wavelet analysis is adopted for denoising, BPANN optimized by PSO is utilized for data analysis and one-dimensional prediction, and Kriging method is used for three-dimensional prediction. Compared with traditional one-dimensional prediction model, three-dimensional model has more real reaction of dissolved oxygen content in crab growth environment. In particular, the merits of PSO are evaluated against genetic algorithm (GA). The root mean square error (RMSE), mean absolute error (MAE), and mean absolute percentage error (MAPE) for PSO model are 0.136445, 0.90534, and 0.15384, respectively, while for the GA model the values are 2.04184, 1.18316, and 0.21014, respectively. Furthermore, results of cross validation experiment show that the average error of this model is 0.0705 (mg/L). Consequently, this study suggests that the prediction model operates in a satisfactory manner.

关键词： DISSOLVED oxygen in water PARTICLE swarm optimization BACK propagation (Artificial intelligence) NEURAL networks (Computer science) KRIGING interpolation algorithms

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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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