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Inverse-free recursive multiresolution algorithms for a data approximation problem

COMPUTERS & MATHEMATICS WITH APPLICATIONS 2016年第4期72卷 1177-1187页

作者： Fortes, M. A. Raydan, M. Sajo-Castelli, A. M. Univ Granada Dept Matemat Aplicada E-18071 Granada Spain Univ Simon Bolivar Dept Comp Cient & Estadist Ap 89000 Caracas 1080A Venezuela

We present inverse-free recursive multiresolution algorithms for data approximation problems based on energy functionals minimization. During the multiresolution process a linear system needs to be solved at each different resolution level, which can be solved with direct or iterative methods. Numerical results are reported, using the sparse Cholesky factorization, for two applications: one concerning the localization of regions in which the energy of a given surface is mostly concentrated, and another one regarding noise reduction of a given dataset. In addition, for large-scale data approximation problems that require a very fine resolution, we discuss the use of the Preconditioned Conjugate Gradient (PCG) iterative method coupled with a specialized monolithic preconditioner, for which one preconditioner is built for the highest resolution level and then the corresponding blocks of that preconditioner are used as preconditioners for the forthcoming lower levels. (C) 2016 Elsevier Ltd. All rights reserved.

关键词： Inverse-free methods multiresolution algorithms Data approximation Powell-Sabin element Noise reduction Energy localization

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A FAST TUNABLE BLURRING ALGORITHM FOR SCATTERED DATA

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SIAM JOURNAL ON SCIENTIFIC COMPUTING 2020年第4期42卷 A2281-A2299页

作者： Robinson, Gregor Grooms, Ian Univ Colorado Dept Appl Math Boulder CO 80309 USA

A blurring algorithm with linear time complexity can reduce the small-scale content of data observed at scattered locations in a spatially extended domain of arbitrary dimension. The method works by forming a Gaussian interpolant of the input data and then convolving the interpolant with a multiresolution Gaussian approximation of the Green function to a differential operator whose spectrum can be tuned for problem-specific considerations. Like conventional blurring algorithms, which the new algorithm generalizes to data measured at locations other than a uniform grid, applications include deblurring and separation of spatial scales. An example illustrates a possible application toward enabling importance sampling approaches to data assimilation of geophysical observations, which are often scattered over a spatial domain, since blurring observations can make particle filters more effective at state estimation of large scales. Another example, motivated by data analysis of dynamics like ocean eddies that have strong separation of spatial scales, uses the algorithm to decompose scattered oceanographic float measurements into large-scale and small-scale components.

关键词： signal processing data assimilation multiresolution algorithms particle filtering

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On some new variational problems for image denoising

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MATHEMATICAL METHODS IN THE APPLIED SCIENCES 2019年第17期42卷 5881-5897页

作者： Amat, Sergio Busquier, Sonia Ruiz, Juan Carlos Trillo, Juan Zouaoui, Sofiane Univ Politecn Cartagena Dept Matemat Aplicada & Estadist Murcia Spain Ecole Super Sci Appl Alger Lab EDPNL & HM ENS Kouba Algiers Algeria

This paper is devoted to image denoising problems using multiresolution schemes related to variational problems. We start with the linear approach of Donoho and Johnstone, that is related to a well known diffusion-type variational problem. In order to improve the behavior of this approach, we propose some new nonlinear variational problems more adapted to the problem of denoising. Moreover, the discretization is performed using nonlinear multiresolution schemes. In particular, we obtain some fast and well adapted schemes for the considered problem of denoising.

关键词： denoising filtering methods image processing multiresolution algorithms nonlinear schemes

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Fast multiresolution algorithms and Their Related Variational Problems for Image Denoising

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JOURNAL OF SCIENTIFIC COMPUTING 2010年第1期43卷 1-23页

作者： Amat, Sergio Ruiz, Juan Carlos Trillo, J. Univ Politecn Cartagena Dept Matemat Aplicada & Estadist Cartagena Spain Ctr Invest Energet Medioambientales & Tecnol Madrid Spain

When considering fast multiresolution techniques for image denoising problems, there are three important aspects. The first one is the choice of the specific multiresolution, the second one the choice of a proper filter function and the third one the choice of the thresholding parameter. Starting from the classical one, namely, linear wavelet algorithms with Donoho and Johnstone's Soft-thresholding with the universal shrinkage parameter, the first aim of this paper is to improve it in the three mentioned directions. Thus, a new nonlinear approach is proposed and analyzed. On the other hand, the linear approach of Donoho and Johnstone is related with a well known variational problem. Our second aim is to find a related variational problem, more adapted to the denoising problem, for the new approach. We would like to mention that the analysis of theoretical properties in a nonlinear setting are usually notoriously more difficult. Finally, a comparison with other approaches, including linear and nonlinear multiresolution schemes, SVD-based schemes and filters with a non-multiresolution nature, is presented.

关键词： multiresolution algorithms Nonlinear schemes Filtered methods Denoising Cell-average discretization

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Optimal quality for image fusion with interpolatory parametric filters

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MATHEMATICS AND COMPUTERS IN SIMULATION 2011年第10期81卷 2307-2316页

作者： Reinoso, J. F. Moncayo, M. Univ Politecn Cartagena UPCT Dept Appl Math & Stat Cartagena Spain Univ Granada Dept Architectural & Engn Graph Express Granada Spain

A possible definition of the term fusion could be a simultaneous combination of output information from several sources. Using complementary data, image fusion may improve quality and consequently interpretability of the result. There are many different ways to proceed with image fusion and several general frameworks have been used for fusing images. Standard image fusion methods are often successful at injecting spatial detail into the multispectral imagery but distort the color information in the process. During the last decade a great amount of research has been devoted concerning the application of wavelet transforms in image fusion. multiresolution decompositions have proved their superiority against other traditional fusion techniques, particularly in terms of minimizing color distortion. By other side, the subject of wavelet has an interdisciplinary relation to subdivision schemes, which has brought on reciprocal interest in both areas. In this work we propose to use a class of subdivision filters or masks depending on a control parameter in order to perform image fusion in the framework of shift invariant discrete multiresolution transforms. As a consequence, we obtain a fusion procedure with a free parameter. This degree of freedom have two main advantages. First, by giving different numerical values to the parameter it is possible to change some features of the resulting image. The second advantage is that it is possible to obtain the value of the parameter in order to solve certain constraint problem formulated in terms of standard measures. The parametric solution of the problem ensures optimal quality of the resulting fused image. In this sense, our approach provides optimal results and it is more dynamic than previous works. (C) 2010 IMACS. Published by Elsevier B.V. All rights reserved.

关键词： Image quality evaluation Image fusion multiresolution algorithms

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Optimal quality for image fusion with interpolatory parametric filters

Optimal quality for image fusion with interpolatory parametr...

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3rd International Conference on French Acronyms of Approximation Methods and Numerical Modelling in Environment and Natural Resources (MAMERN09)

作者： Reinoso, J. F. Moncayo, M. Univ Politecn Cartagena UPCT Dept Appl Math & Stat Cartagena Spain Univ Granada Dept Architectural & Engn Graph Express Granada Spain

关键词： Image quality evaluation Image fusion multiresolution algorithms

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Parallel robust relaxation algorithm for automatic stereo analysis

Parallel robust relaxation algorithm for automatic stereo an...

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SPIE Conference on Parallel and Distributed Methods for Image Processing II

作者： Palaniappan, K Vass, J Zhuang, XH Univ Missouri Dept Comp Engn & Comp Sci Multimedia Commun & Visualizat Lab Columbia MO 65211 USA

ISBN: (纸本)0819429074

A parallel robust relaxation algorithm is proposed to improve the detection and correction of illegal disparities encountered in the automatic stereo analysis (ASA) algorithm. Outliers and noisy matches from correlation-based BSA matching are improved by relaxation labeling and robust statistical methods at each stage of the multiresolution coarse-to-fine analysis. A parallel version of the relaxation labeling algorithm has been implemented for the MasPar supercomputer. The performance scales quite linearly with the number of processing elements and scales better than linear with increasing work load. The algorithm is highly scalable both as the number of processors are increased for solving a fixed size problem and also as the size of the problem increases.

关键词： parallel stereo correlation matching multiresolution algorithms parallel relaxation labeling robust estimation

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Silica under very large positive and negative pressures: Molecular dynamics simulations on parallel computers

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INTERNATIONAL JOURNAL OF THERMOPHYSICS 1996年第1期17卷 169-178页

作者： Vashishta, P Kalia, RK Nakano, A Jin, W LOUISIANA STATE UNIV DEPT COMP SCIBATON ROUGELA 70803

A highly efficient multiresolution algorithm has been developed to carry out large-scale molecular dynamics (MD) simulations for systems with long-range Coulomb and three-body covalent interactions. The algorithm combines the reduced cell and fast multipole methods and multiple time-step approach. Pressure-induced structural transformation, loss of intermediate range order, and dynamical correlations in SiO2 glass are investigated with the molecular-dynamics method. At twice the normal density, the Si-O bond length increases, the Si-O coordination changes from 4 to 6, and the O-Si-O band-angle changes from 109 to 90 degrees. This is a tetrahedral-to-octahedral transformation, which was reported by Meade, Hemley, and Mao. Results for phonon density of states also reveal significant changes at high pressures. The multiresolution MD approach has been used to investigate the structural properties and mechanical failure in microporous silica. Structural correlations are characterized by the fractal dimension, internal surface area, and pore surface-to-volume ratio. Critical behavior at fracture is analyzed in terms of pore percolation, and kinetic roughening of fractured surface is also investigated.

关键词： densified silica fast multipole method fracture high pressure intermediate range order kinetic roughening molecular dynamics multiresolution algorithms parallel computing porous silica structural transformations

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multiresolution HOUGH TRANSFORM - AN EFFICIENT METHOD OF DETECTING PATTERNS IN IMAGES

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IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE 1992年第11期14卷 1090-1095页

作者： ATIQUZZAMAN, M KING FAHD UNIV PETR & MINERALS DEPT ELECT ENGNDHAHRANSAUDI ARABIA

The Hough transform is highly compute bound and demands a large amount of storage. In this correspondence, a novel multiresolution implementation of the Hough transform has been proposed. To reduce the computing time, it exploits the reduced information content of multiresolution images and accumulator arrays and uses a simple peak detection algorithm. Logarithmic parameter-range reduction ensures faster convergence than other methods. The algorithm takes care of discretization errors.

关键词： DISCRETIZATION ERRORS HOUGH TRANSFORM IMAGE PROCESSING multiresolution algorithms PATTERN RECOGNITION

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USING CHROMATIC INFORMATION IN DENSE STEREO CORRESPONDENCE

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PATTERN RECOGNITION 1992年第4期25卷 367-383页

作者： JORDAN, JR BOVIK, AC UNIV TEXAS DEPT ELECT & COMP ENGNVIS SYST LABAUSTINTX 78712

The use of chromatic information in dense stereo correspondence is investigated. Specifically, the chromatic photometric constraint, which is used to specify a mathematical optimality criterion for solving the dense stereo correspondence problem, is developed. The result is a theoretical construction for developing dense stereo correspondence algorithms which use chromatic information. The efficacy of using chromatic information via this construction is tested by implementing single- and multi-resolution versions of a stereo correspondence algorithm that uses simulated annealing as a means of solving the optimization problem, Results demonstrate that the use of chromatic information can significantly improve the performance of dense stereo correspondence.

关键词： COLOR STEREO VISION DENSE STEREO CORRESPONDENCE COLOR FEATURES SIMULATED ANNEALING multiresolution algorithms

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