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Journal articles on the topic 'Multiresolution'

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Published: 4 June 2021

Last updated: 4 May 2024

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1

Kannan, S. Thabasu, and S. Azhagu Senthil. "Evaluvation of Multiresolution Watermarking Algorithm." International Journal of Advanced Research in Computer Science and Software Engineering 7, no. 8 (August 30, 2017): 85. http://dx.doi.org/10.23956/ijarcsse.v7i8.29.

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Now-a-days watermarking plays a pivotal role in most of the industries for providing security to their own as well as hired or leased data. This paper its main aim is to study the multiresolution watermarking algorithms and also choosing the effective and efficient one for improving the resistance in data compression. Computational savings from such a multiresolution watermarking framework is obvious. The multiresolutional property makes our watermarking scheme robust to image/video down sampling operation by a power of two in either space or time. There is no common framework for multiresolutional digital watermarking of both images and video. A multiresolution watermarking based on the wavelet transformation is selected in each frequency band of the Discrete Wavelet Transform (DWT) domain and therefore it can resist the destruction of image processing. The rapid development of Internet introduces a new set of challenging problems regarding security. One of the most significant problems is to prevent unauthorized copying of digital production from distribution. Digital watermarking has provided a powerful way to claim intellectual protection. We proposed an idea for enhancing the robustness of extracted watermarks. Watermark can be treated as a transmitted signal, while the destruction from attackers is regarded as a noisy distortion in channel. For the implementation, we have used minimum nine coordinate positions. The watermarking algorithms to be taken for this study are Corvi algorithm and Wang algorithm. In all graph, we have plotted X axis as peak signal to noise ratio (PSNR) and y axis as Correlation with original watermark. The threshold value ά is set to 5. The result is smaller than the threshold value then it is feasible, otherwise it is not.

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2

Yanjun Zhao and S. Belkasim. "Multiresolution Fourier Descriptors for Multiresolution Shape Analysis." IEEE Signal Processing Letters 19, no. 10 (October 2012): 692–95. http://dx.doi.org/10.1109/lsp.2012.2210040.

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3

San Antolín, Angel. "On translation invariant multiresolution analysis." Glasnik Matematicki 49, no. 2 (December 18, 2014): 377–94. http://dx.doi.org/10.3336/gm.49.2.11.

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4

Chiou-Ting Hsu and Ja-Ling Wu. "Multiresolution mosaic." IEEE Transactions on Consumer Electronics 42, no. 4 (1996): 981–90. http://dx.doi.org/10.1109/30.555800.

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5

Starck, Jean-Luc, and Albert Bijaoui. "Multiresolution deconvolution." Journal of the Optical Society of America A 11, no. 5 (May 1, 1994): 1580. http://dx.doi.org/10.1364/josaa.11.001580.

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6

Meyers, David. "Multiresolution Tiling." Computer Graphics Forum 13, no. 5 (December 1994): 325–40. http://dx.doi.org/10.1111/1467-8659.1350325.

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7

Xiaoqiang Lu and Xuelong Li. "Multiresolution Imaging." IEEE Transactions on Cybernetics 44, no. 1 (January 2014): 149–60. http://dx.doi.org/10.1109/tcyb.2013.2286496.

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8

Zhang, Liyan, Jian Ma, Bin Ran, and Lixin Yan. "Traffic Multiresolution Modeling and Consistency Analysis of Urban Expressway Based on Asynchronous Integration Strategy." Modelling and Simulation in Engineering 2017 (2017): 1–19. http://dx.doi.org/10.1155/2017/3694791.

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The paper studies multiresolution traffic flow simulation model of urban expressway. Firstly, compared with two-level hybrid model, three-level multiresolution hybrid model has been chosen. Then, multiresolution simulation framework and integration strategies are introduced. Thirdly, the paper proposes an urban expressway multiresolution traffic simulation model by asynchronous integration strategy based on Set Theory, which includes three submodels: macromodel, mesomodel, and micromodel. After that, the applicable conditions and derivation process of the three submodels are discussed in detail. In addition, in order to simulate and evaluate the multiresolution model, “simple simulation scenario” of North-South Elevated Expressway in Shanghai has been established. The simulation results showed the following.(1)Volume-density relationships of three submodels are unanimous with detector data.(2)When traffic density is high, macromodel has a high precision and smaller error and the dispersion of results is smaller. Compared with macromodel, simulation accuracies of micromodel and mesomodel are lower but errors are bigger.(3)Multiresolution model can simulate characteristics of traffic flow, capture traffic wave, and keep the consistency of traffic state transition. Finally, the results showed that the novel multiresolution model can have higher simulation accuracy and it is feasible and effective in the real traffic simulation scenario.

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9

Li, Ai Min, and Hai Bo Tian. "A Multiresolution Fairing Approach for NURBS Curves." Applied Mechanics and Materials 215-216 (November 2012): 1205–8. http://dx.doi.org/10.4028/www.scientific.net/amm.215-216.1205.

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Curve fairing has an important influence on curve editing and geometric modeling. Though there has been several different kinds of fairing methods, Multiresolution curve fairing has higher efficiency and simpler algorithms. Different from existing multiresolution curve fairing, a new multiresolution approach is presented based on non-uniform semiorthogonal B-spline wavelets, which can be applied for NURBS curve fairing. It has no restriction to B-spline curves’ knot sequence. This method effectively overcomes the limit of uniform or quasi-uniform B-spline wavelets for fairing. A detailed example is given to show the effectiveness of this multiresolution fairing method.

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10

Li, Ai Min, Wei Guo, Hai Bo Tian, and Fa Rong Kou. "Wavelet-Based Multiresolution NURBS Curve Fairing." Advanced Materials Research 314-316 (August 2011): 1562–65. http://dx.doi.org/10.4028/www.scientific.net/amr.314-316.1562.

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A multiresolution approach is presented for NURBS curve fairing based on nonuniform semiorthogonal B-spline wavelets built. This method provides greater flexibility and applicability than uniform B-spline wavelets for multiresolution curve fairing. An example is presented to validate effectiveness of this multiresolution fairing method. Furthermore, the algorithm can be easily applied to NURBS curves in three dimensions as well as in two.

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11

Effros, M., and D. Dugatkin. "Multiresolution Vector Quantization." IEEE Transactions on Information Theory 50, no. 12 (December 2004): 3130–45. http://dx.doi.org/10.1109/tit.2004.838381.

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12

Lemma, A. N., A. J. van der Veen, and E. F. Deprettere. "Multiresolution ESPRIT algorithm." IEEE Transactions on Signal Processing 47, no. 6 (June 1999): 1722–26. http://dx.doi.org/10.1109/78.765149.

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13

Rakić, Dušan. "Multiresolution expansion in." Integral Transforms and Special Functions 20, no. 3-4 (April 2009): 231–38. http://dx.doi.org/10.1080/10652460802568143.

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14

Badoual, Anais, Daniel Schmitter, Virginie Uhlmann, and Michael Unser. "Multiresolution Subdivision Snakes." IEEE Transactions on Image Processing 26, no. 3 (March 2017): 1188–201. http://dx.doi.org/10.1109/tip.2016.2644263.

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15

Domingues, Margarete O., Sônia M. Gomes, Olivier Roussel, and Kai Schneider. "Adaptive multiresolution methods." ESAIM: Proceedings 34 (December 2011): 1–96. http://dx.doi.org/10.1051/proc/201134001.

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16

Xia, Kelin, Zhixiong Zhao, and Guo-Wei Wei. "Multiresolution Topological Simplification." Journal of Computational Biology 22, no. 9 (September 2015): 887–91. http://dx.doi.org/10.1089/cmb.2015.0104.

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17

Combettes, P. L., and J. C. Pesquet. "Convex multiresolution analysis." IEEE Transactions on Pattern Analysis and Machine Intelligence 20, no. 12 (1998): 1308–18. http://dx.doi.org/10.1109/34.735804.

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18

Wang, Guoqiu. "Multiresolution sampling applications." Optical Engineering 37, no. 6 (June 1, 1998): 1703. http://dx.doi.org/10.1117/1.601796.

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19

Wilson, R. "Multiresolution image modelling." Electronics & Communication Engineering Journal 9, no. 2 (April 1, 1997): 90–96. http://dx.doi.org/10.1049/ecej:19970206.

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20

Howell, J. F., and L. Mahrt. "Multiresolution Flux Decomposition." Boundary-Layer Meteorology 83, no. 1 (April 1997): 117–37. http://dx.doi.org/10.1023/a:1000210427798.

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21

Fosdick, Bailey K., Tyler H. McCormick, Thomas Brendan Murphy, Tin Lok James Ng, and Ted Westling. "Multiresolution Network Models." Journal of Computational and Graphical Statistics 28, no. 1 (November 5, 2018): 185–96. http://dx.doi.org/10.1080/10618600.2018.1505633.

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22

Fernandez, Jose David, and Joel de Coninck. "Multiresolution layered manufacturing." Rapid Prototyping Journal 25, no. 1 (January 7, 2019): 87–94. http://dx.doi.org/10.1108/rpj-07-2017-0146.

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Purpose Two-photon polymerization (TPP) has become one of the most popular techniques for stereolithography at very high resolutions. When printing relatively large structures at high resolutions, one of the main limiting factors is the printing time. The purpose of this paper is to present a new slicing algorithm to minimize printing times. Design/methodology/approach Typically, slicing algorithms used for TPP do not take into account the fact that TPP can print at a range of resolutions (i.e. with different heights and diameters) by varying parameters such as exposure time, laser power, photoresist properties and optical arrangements. This work presents multiresolution layered manufacturing (MLM), a novel slicing algorithm that processes 3D structures to separate parts manufacturable at low resolution from those that require a higher resolution. Findings MLM can significantly reduce the printing time of 3D structures at high resolutions. The maximum theoretical speed-up depends on the range of printing resolutions, but the effective speed-up also depends on the geometry of each 3D structure. Research limitations/implications MLM opens the possibility to significantly decrease printing times, potentially opening the use of TPP to new applications in many disciplines such as microfluidics, metamaterial research or wettability. Originality/value There are many instances of previous research on printing at several resolutions. However, in most cases, the toolpaths have to be manually arranged. In some cases, previous research also automates the generation of toolpaths, but they are limited in various ways. MLM is the first algorithm to comprehensively solve this problem for a wide range of true 3D structures.

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23

Chen, Jun, Sorina Dumitrescu, Ying Zhang, and Jia Wang. "Robust Multiresolution Coding." IEEE Transactions on Communications 58, no. 11 (November 2010): 3186–95. http://dx.doi.org/10.1109/tcomm.2010.093010.100024.

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24

Jia, Rong-Qing, and Zuowei Shen. "Multiresolution and wavelets." Proceedings of the Edinburgh Mathematical Society 37, no. 2 (June 1994): 271–300. http://dx.doi.org/10.1017/s0013091500006076.

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Multiresolution is investigated on the basis of shift-invariant spaces. Given a finitely generated shift-invariant subspace S of L2(ℝd), let Sk be the 2k-dilate of S (k∈ℤ). A necessary and sufficient condition is given for the sequence {Sk}k∈ℤ to fom a multiresolution of L2(ℝd). A general construction of orthogonal wavelets is given, but such wavelets might not have certain desirable properties. With the aid of the general theory of vector fields on spheres, it is demonstrated that the intrinsic properties of the scaling function must be used in constructing orthogonal wavelets with a certain decay rate. When the scaling function is skew-symmetric about some point, orthogonal wavelets and prewavelets are constructed in such a way that they possess certain attractive properties. Several examples are provided to illustrate the general theory.

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25

Brunet, P., and R. Scopigno. "Multiresolution geometric models." Computer-Aided Design 32, no. 13 (November 2000): 751–52. http://dx.doi.org/10.1016/s0010-4485(00)00066-x.

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26

Bajcsy, Ruzena, and Stane Kovačič. "Multiresolution elastic matching." Computer Vision, Graphics, and Image Processing 46, no. 1 (April 1989): 1–21. http://dx.doi.org/10.1016/s0734-189x(89)80014-3.

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27

Engel, Joachim. "The multiresolution histogram." Metrika 46, no. 1 (January 1997): 41–57. http://dx.doi.org/10.1007/bf02717165.

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28

Bajcsy, Ruzena. "Multiresolution elastic matching." Computer Vision, Graphics, and Image Processing 45, no. 1 (January 1989): 132. http://dx.doi.org/10.1016/0734-189x(89)90082-0.

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29

Harrison, Robert J., George I. Fann, Zhengting Gan, Takeshi Yanai, Shinichiro Sugiki, Ariana Beste, and Gregory Beylkin. "Multiresolution computational chemistry." Journal of Physics: Conference Series 16 (January 1, 2005): 243–46. http://dx.doi.org/10.1088/1742-6596/16/1/032.

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30

Stein, Charles S., and Lewis E. Hitchner. "The Multiresolution Dissolve." SMPTE Journal 97, no. 12 (December 1988): 977–84. http://dx.doi.org/10.5594/j02848.

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31

Kemeny, S. E., R. Panicacci, B. Pain, L. Matthies, and E. R. Fossum. "Multiresolution image sensor." IEEE Transactions on Circuits and Systems for Video Technology 7, no. 4 (1997): 575–83. http://dx.doi.org/10.1109/76.611169.

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32

Liu, Yuying, Colin Ponce, Steven L. Brunton, and J. Nathan Kutz. "Multiresolution convolutional autoencoders." Journal of Computational Physics 474 (February 2023): 111801. http://dx.doi.org/10.1016/j.jcp.2022.111801.

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33

Kemal Ekenel, Hazim, and Bülent Sankur. "Multiresolution face recognition." Image and Vision Computing 23, no. 5 (May 2005): 469–77. http://dx.doi.org/10.1016/j.imavis.2004.09.002.

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34

Massopust, Peter R. "Generalized Multiresolution Schemes." Journal of Mathematical Analysis and Applications 221, no. 2 (May 1998): 574–94. http://dx.doi.org/10.1006/jmaa.1998.5917.

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35

LIVNY, YOTAM, NETA SOKOLOVSKY, and JIHAD EL-SANA. "DUAL ADAPTIVE PATHS FOR MULTIRESOLUTION HIERARCHIES." International Journal of Image and Graphics 07, no. 02 (April 2007): 273–90. http://dx.doi.org/10.1142/s0219467807002726.

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The recent increase in the generated polygonal dataset sizes has outpaced the performance of graphics hardware. Several solutions such as multiresolution hierarchies and level-of-detail rendering have been developed to bridge the increasing gap. However, the discrete levels of detail generate annoying popping effects, the preliminaries multiresolution schemes cannot perform drastic changes on the selected level of detail within the span of small number of frames, and the current cluster-based hierarchies suffer from the high-detailed representation of the boundaries between clusters. In this paper, we are presenting a novel approach for multiresolution hierarchy that supports dual paths for run-time adaptive simplification — fine and coarse. The proposed multiresolution hierarchy is based on the fan-merge operator and its reverse operator fan-split. The coarse simplification path is achieved by directly applying fan-merge/split, while the fine simplification route is performed by executing edge-collapse/vertex-split one at a time. The sequence of the edge-collapses/vertex-splits is encoded implicitly by the order of the children participating in the fan-merge/split operator. We shall refer to this multiresolution hierarchy as fan-hierarchy. Fan-hierarchy provides a compact data structure for multiresolution hierarchy, since it stores 7/6 pointers, on the average, instead of 3 pointers for each node. In addition, the resulting depth of the fan-hierarchy is usually smaller than the depth of hierarchies generated by edge-collapse based multiresolution schemes. It is also important to note that fan-hierarchy inherently utilizes fan representation for further acceleration of the rendering process.

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36

Sharma, Vikram, and P. Manchanda. "WAVELET PACKETS ASSOCIATED WITH NONUNIFORM MULTIRESOLUTION ANALYSIS ON POSITIVE HALF LINE." Asian-European Journal of Mathematics 06, no. 01 (March 2013): 1350007. http://dx.doi.org/10.1142/s1793557113500071.

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Gabardo and Nashed [Nonuniform multiresolution analysis and spectral pairs, J. Funct. Anal.158 (1998) 209–241] introduced the Nonuniform multiresolution analysis (NUMRA) whose translation set is not a group. Farkov [Orthogonal p-wavelets on ℝ+, in Proc. Int. Conf. Wavelets and Splines (St. Petersburg State University, St. Petersburg, 2005), pp. 4–26] studied multiresolution analysis (MRA) on positive half line and constructed associated wavelets. Meenakshi et al. [Wavelets associated with Nonuniform multiresolution analysis on positive half line, Int. J. Wavelets, Multiresolut. Inf. Process.10(2) (2011) 1250018, 27pp.] studied NUMRA on positive half line and proved the analogue of Cohen's condition for the NUMRA on positive half line. We construct the associated wavelet packets for such an MRA and study its properties.

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37

BACCOU, J., and J. LIANDRAT. "POSITION-DEPENDENT LAGRANGE INTERPOLATING MULTIRESOLUTIONS." International Journal of Wavelets, Multiresolution and Information Processing 05, no. 04 (July 2007): 513–39. http://dx.doi.org/10.1142/s0219691307001884.

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This paper is devoted to the construction of interpolating multiresolutions using Lagrange polynomials and incorporating a position dependency. It uses the Harten's framework21 and its connection to subdivision schemes. Convergence is first emphasized. Then, plugging the various ingredients into the wavelet multiresolution analysis machinery, the construction leads to position-dependent interpolating bases and multi-scale decompositions that are useful in many instances where classical translation-invariant frameworks fail. A multivariate generalization is proposed and analyzed. We investigate applications to the reduction of the so-called Gibbs phenomenon for the approximation of locally discontinuous functions and to the improvement of the compression of locally discontinuous 1D signals. Some applications to image decomposition are finally presented.

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38

Curry, Eva. "Low-Pass Filters and Scaling Functions for Multivariable Wavelets." Canadian Journal of Mathematics 60, no. 2 (April 1, 2008): 334–47. http://dx.doi.org/10.4153/cjm-2008-016-1.

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AbstractWe show that a characterization of scaling functions for multiresolution analyses given by Hernández and Weiss and that a characterization of low-pass filters given by Gundy both hold for multivariable multiresolution analyses.

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39

Du, Shu De, and Bao Xian Lv. "The Characterization of Multiple Harmanic Riesz Bases of Affine Subspaces and Applications." Applied Mechanics and Materials 321-324 (June 2013): 2371–74. http://dx.doi.org/10.4028/www.scientific.net/amm.321-324.2371.

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An information system is any combination of information technology and people's act- ivities that support operations, management and decision making. Information science focuses on understanding problems from the perspective of the stakeholders involved and then applying information and other technologies as needed. The definition of multiple harmonic frames for subs -paces with integer translation is proposed. The notion of a generalized multiresolution structure of is also introduced. The construction of a generalized multiresolution structure of Paley -Wiener subspaces of is investigated. The pyramid decomposition scheme is derived based on a generalized multiresolution structure.

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Kapoor, G. P., and Srijanani Anurag Prasad. "Multiresolution Analysis Based on Coalescence Hidden-Variable Fractal Interpolation Functions." International Journal of Computational Mathematics 2014 (December 11, 2014): 1–7. http://dx.doi.org/10.1155/2014/531562.

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Multiresolution analysis arising from Coalescence Hidden-variable Fractal Interpolation Functions (CHFIFs) is developed. The availability of a larger set of free variables and constrained variables with CHFIF in multiresolution analysis based on CHFIFs provides more control in reconstruction of functions in L2(R) than that provided by multiresolution analysis based only on Affine Fractal Interpolation Functions (AFIFs). Our approach consists of introduction of the vector space of CHFIFs, determination of its dimension and construction of Riesz bases of vector subspaces Vk, k∈Z, consisting of certain CHFIFs in L2(R)∩C0(R).

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41

Elber, Gershon. "Multiresolution Curve Editing With Linear Constraints*." Journal of Computing and Information Science in Engineering 1, no. 4 (October 1, 2001): 347–55. http://dx.doi.org/10.1115/1.1430679.

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The use of multiresolution control toward the editing of freeform curves and surfaces has already been recognized as a valuable modeling tool [1–3]. Similarly, in contemporary computer aided geometric design, the use of constraints to precisely prescribe freeform shape is considered an essential capability [4,5]. This paper presents a scheme that combines multiresolution control with linear constraints into one framework, allowing one to perform multiresolution manipulation of nonuniform B-spline curves, while specifying and satisfying various linear constraints on the curves. Positional, tangential, and orthogonality constraints are all linear and can be easily incorporated into a multiresolution freeform curve editing environment, as will be shown. Moreover, we also show that the symmetry as well as the area constraints can be reformulated as linear constraints and similarly incorporated. The presented framework is extendible and we also portray this same framework in the context of freeform surfaces.

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42

Mair, Christina, Natalie Sumetsky, Andrew Gaidus, Paul J. Gruenewald, and William R. Ponicki. "Multiresolution Analyses of Neighborhood Correlates of Crime: Smaller Is Not Better." American Journal of Epidemiology 190, no. 1 (July 23, 2020): 150–60. http://dx.doi.org/10.1093/aje/kwaa157.

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Abstract Population analyses of the correlates of neighborhood crime implicitly assume that a single spatial unit can be used to assess neighborhood effects. However, no single spatial unit may be suitable for analyses of the many social determinants of crime. Instead, effects may appear at multiple spatial resolutions, with some determinants acting broadly, others locally, and still others as some function of both global and local conditions. We provide a multiresolution spatial analysis that simultaneously examines US Census block, block group, and tract effects of alcohol outlets and drug markets on violent crimes in Oakland, California, incorporating spatial lag effects at the 2 smaller spatial resolutions. Using call data from the Oakland Police Department from 2010–2015, we examine associations of assaults, burglaries, and robberies with multiple resolutions of alcohol outlet types and compare the performance of single (block-level) models with that of multiresolution models. Multiresolution models performed better than the block models, reflected in improved deviance and Watanabe-Akaike information criteria and well-supported multiresolution associations. By considering multiple spatial scales and spatial lags in a Bayesian framework, researchers can explore multiresolution processes, providing more detailed tests of expectations from theoretical models and leading the way to more effective intervention efforts.

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43

Chen, Qing Jiang, and Gai Hu. "A Study of Binary Minimum-Energy Shortly Supported Wavelet Frames Associated with a Scaling Function." Advanced Materials Research 219-220 (March 2011): 500–503. http://dx.doi.org/10.4028/www.scientific.net/amr.219-220.500.

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Frames have become the focus of active research field, both in theory and in applications. In the article, the binary minimum-energy wavelet frames and frame multiresolution resolution are introduced. A precise existence criterion for minimum-energy frames in terms of an ineqity conditi- -on on the Laurent poly-nomial symbols of the filter functions is provided. An explicit formula for designing minimum-energy frames is also established. The sufficient condition for the existence of affine pseudoframes is obtained by virtue of a generalized multiresolution analysis. The pyramid de -composition scheme is established based on such a generalized multiresolution structure.

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Lim, Jae Kun. "Gramian analysis of multivariate frame multiresolution analyses." Bulletin of the Australian Mathematical Society 66, no. 2 (October 2002): 291–300. http://dx.doi.org/10.1017/s0004972700040132.

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We perform a Gramian analysis of a frame multiresolution analysis to give a condition for it to admit a minimal wavelet set and to show that the frame bounds of the natural generator for the wavelet space of a degenerate frame multiresolution analysis shrink.

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45

MEENAKSHI, P. MANCHANDA, and A. H. SIDDIQI. "WAVELETS ASSOCIATED WITH NONUNIFORM MULTIRESOLUTION ANALYSIS ON POSITIVE HALF-LINE." International Journal of Wavelets, Multiresolution and Information Processing 10, no. 02 (March 2012): 1250018. http://dx.doi.org/10.1142/s021969131250018x.

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Gabardo and Nashed have studied nonuniform multiresolution analysis based on the theory of spectral pairs in a series of papers, see Refs. 4 and 5. Farkov,3 has extended the notion of multiresolution analysis on locally compact Abelian groups and constructed the compactly supported orthogonal p-wavelets on L2(ℝ+). We have considered the nonuniform multiresolution analysis on positive half-line. The associated subspace V0 of L2(ℝ+) has an orthonormal basis, a collection of translates of the scaling function φ of the form {φ(x ⊖ λ)}λ∈Λ+ where Λ+ = {0, r/N} + ℤ+, N > 1 (an integer) and r is an odd integer with 1 ≤ r ≤ 2N - 1 such that r and N are relatively prime and ℤ+ is the set of non-negative integers. We find the necessary and sufficient condition for the existence of associated wavelets and derive the analogue of Cohen's condition for the nonuniform multiresolution analysis on the positive half-line.

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46

Huang, Yong Yi, and Jian Feng Zhou. "The Characters of Dual Harmonic Frames of Subspaces and Applications in Signal Processing Theory." Applied Mechanics and Materials 457-458 (October 2013): 731–35. http://dx.doi.org/10.4028/www.scientific.net/amm.457-458.731.

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Digital signal processing is the processing of digitized discrete-time samp-led signals. Processing is done by general-purpose computers or by digital circuits such as ASICs, field-programmable gate arrays or specialized digital signal processors. Information science focuses on understanding problems from the perspective of the stakeholders involved and then applying information and other technologies as needed. The definition of multiple pseudofames for subspaces with integer translation is proposed. The notion of a generalized multiresolution structure (GMS) of is also introduced. The construction of a generalized multiresolution structure of Paley-Wiener subspaces of is investigated. The pyramid decomposition scheme is derived based on a generalized multiresolution structure.

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47

Yiwang, Chen, Ni Jiazheng, Liu Yawen, Dong Xiaohua, and Zhang Pin. "The Alternating Direction Implicit Body of Revolution Multiresolution Time Domain Method with Convolution Perfect Matched Layer." Mathematical Problems in Engineering 2017 (2017): 1–8. http://dx.doi.org/10.1155/2017/2073563.

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Overmuch memory and time of CPU have been taken by multiresolution time domain (MRTD) method in three-dimension issues. In order to solve this problem, the alternating direction implicit body of revolution multiresolution time domain (ADI-BOR-MRTD) scheme is presented. Firstly, based on body of revolution finite difference time domain (BOR-FDTD) method, equations of body of revolution multiresolution time domain (BOR-MRTD) method are implemented. Then alternating direction implicit (ADI) is introduced into BOR-MRTD method. Lastly, convolution perfect matched layer (CPML) is applied for ADI-BOR-MRTD method. Numerical results demonstrate that ADI-BOR-MRTD method saves more memory and time of CPU than FDTD and MRTD methods.

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48

Cheng, Bing, and Xiaokun Zhu. "A Multiresolution Approximation Theory of Fractal Transform." Fractals 05, supp01 (April 1997): 173–86. http://dx.doi.org/10.1142/s0218348x97000747.

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In this paper, we show that the fractal transform (FT) constitutes a multiresolution approximation to the square-integrable space L2(Td) for d≥1, where T is the interval (-∞,∞). This provides a theoretical basis for the successful applications of the fractal transform algorithms in signal/image encoding. There are many similarities between fractal-based and wavelet-based approximations. However, they are undamentally different from each other in many aspects. Fractal-based multiresolution approximation to signals/images is by a way of self-increasing model complexity, and wavelet-based multiresolution approximation to signals/images is by a way of decomposing data complexity into single (time domain) components.

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Tan, Xiaojing, Ming Zou, and Xiqin He. "Target Recognition in SAR Images Based on Multiresolution Representations with 2D Canonical Correlation Analysis." Scientific Programming 2020 (February 24, 2020): 1–9. http://dx.doi.org/10.1155/2020/7380790.

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This study proposes a synthetic aperture radar (SAR) target-recognition method based on the fused features from the multiresolution representations by 2D canonical correlation analysis (2DCCA). The multiresolution representations were demonstrated to be more discriminative than the solely original image. So, the joint classification of the multiresolution representations is beneficial to the enhancement of SAR target recognition performance. 2DCCA is capable of exploiting the inner correlations of the multiresolution representations while significantly reducing the redundancy. Therefore, the fused features can effectively convey the discrimination capability of the multiresolution representations while relieving the storage and computational burdens caused by the original high dimension. In the classification stage, the sparse representation-based classification (SRC) is employed to classify the fused features. SRC is an effective and robust classifier, which has been extensively validated in the previous works. The moving and stationary target acquisition and recognition (MSTAR) data set is employed to evaluate the proposed method. According to the experimental results, the proposed method could achieve a high recognition rate of 97.63% for the 10 classes of targets under the standard operating condition (SOC). Under the extended operating conditions (EOC) like configuration variance, depression angle variance, and the robustness of the proposed method are also quantitively validated. In comparison with some other SAR target recognition methods, the superiority of the proposed method can be effectively demonstrated.

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Bugya, Titusz, and Ákos Halmai. "The Multiresolution Image Format." Journal of Geographic Information System 05, no. 01 (2013): 87–95. http://dx.doi.org/10.4236/jgis.2013.51009.

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