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1. Small Support Spline Riesz Wavelets in Low Dimensions | |||
HAN Bin,MO Qun,SHEN Zuowei | |||
Mathematics 26 January 2011 | |||
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Abstract:B.~Han and Z.~Shen constructed afamily of univariate short support Riesz waveletsfrom uniform B-splines in 2006. A bivariate spline Riesz wavelet basis fromthe Loop scheme was derived by B.~Han and Z.~Shen in 2005.Motivated bythese two papers, we develop in this article ageneral theory and a construction method to derive small supportRiesz wavelets in low dimensions from refinable functions. Inparticular, we obtain small support spline Riesz wavelets frombivariate and trivariate box splines. Small support Riesz waveletsare desirable for developing efficient algorithms in variousapplications. For example, the short support Riesz wavelets constructed byB.~Han and Z.~Shen were used in a surface fitting algorithm byM.J.~Johnson, Z.~Shen and Y.H.~Xu in 2009, and the Riesz wavelet basis from the Loop scheme wasused in a very efficient geometric mesh compression algorithm byA. Khodakovsky, P. Schr"oder and W. Sweldens in 2000. | |||
TO cite this article:HAN Bin,MO Qun,SHEN Zuowei. Small Support Spline Riesz Wavelets in Low Dimensions[OL].[26 January 2011] http://en.paper.edu.cn/en_releasepaper/content/4408648 |
2. Remark on the Restricted Isometry Property in Orthogonal Matching Pursuit | |||
MO Qun,SHEN Yi | |||
Mathematics 26 January 2011 | |||
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Abstract:This paper demonstrates theoretically that if the restrictedisometry constant of the compressed sensing matrixsatisfies a sufficient condition,then a greedy algorithm called Orthogonal Matching Pursuit (OMP) canrecover a signal with K nonzero entries in K iterations. Incontrast, matrices are also constructed with restricted isometryconstant satisfying a stronger conditionsuch that OMP can not recover K-sparse x in K iterations. Thisresult shows that the conjecture given by Dai and Milenkovic is true. | |||
TO cite this article:MO Qun,SHEN Yi. Remark on the Restricted Isometry Property in Orthogonal Matching Pursuit[OL].[26 January 2011] http://en.paper.edu.cn/en_releasepaper/content/4408549 |
3. ON BOUNDARY BEHAVIOR OF THE CAUCHY TYPE INTEGRAL IN HYPERCOMPLEX ANALYSIS | |||
Du Jinyuan | |||
Mathematics 04 May 2010 | |||
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Abstract:We survey the researches of the boundary behavior for the Cauchy type integrals defined on a smooth closed surface in the Euclidean space with values on the Clifford algebra, or defined on the distinguished boundary of the direct product of two domains with values on the universal Clifford algebra, which includes Sochocki-Plemelj formulae and Privalov-Muskhelishvili theorems, Poincare-Bertrand formulae. Then some boundary value problems and singular integral equation in Clifford analysis are introduced. | |||
TO cite this article:Du Jinyuan. ON BOUNDARY BEHAVIOR OF THE CAUCHY TYPE INTEGRAL IN HYPERCOMPLEX ANALYSIS[OL].[ 4 May 2010] http://en.paper.edu.cn/en_releasepaper/content/42553 |
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