摘要: This paper constructs translation-invariant operators on L 2 .R d /, which are Lipschitz-continuous to the action of diffeomorphisms. A scattering propagator is a path-ordered product nonlinear and noncommuting operators, each computes modulus wavelet transform. local integration defines windowed transform, proved be C As window size increases, it converges transform that translation invariant. Scattering coefficients also provide representations stationary processes. Expected values depend upon high-order moments can discriminate processes having same power spectrum. extended .G/, where G compact Lie group, invariant under G. Combining / .SO.d// translation- rotation-invariant /. © 2012 Wiley Periodicals, Inc.
arxiv-vanity.com
core.ac.uk参考文章(22)
Yves Meyer, Wavelets and Operators ,(1993)
Michael Frazier, Björn Jawerth, Guido Weiss, Littlewood-Paley Theory and the Study of Function Spaces CBMS Regional Conference Series in Mathematics. ,vol. 79, ,(1991) , 10.1090/CBMS/079
Stephane Mollai, Recursive interferometric representations european signal processing conference. pp. 716- 720 ,(2010)
Peter J. Olver, Equivalence, invariants, and symmetry ,(1995)
Elias M. Stein, Topics in Harmonic Analysis Related to the Littlewood-Paley Theory. ,(1970)
Michael E. Glinsky, A new perspective on renormalization: invariant actions, a dynamical DNA ,(2011)
Elias Menachem Stein, Timothy S Murphy, Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals ,(1993)
Daryl Geller, Isaac Z. Pesenson, Band-Limited Localized Parseval Frames and Besov Spaces on Compact Homogeneous Manifolds Journal of Geometric Analysis. ,vol. 21, pp. 334- 371 ,(2011) , 10.1007/S12220-010-9150-3
Theodore Frankel, The Geometry of Physics: An Introduction ,(2012)
Alain Trouvé, Laurent Younes, Local Geometry of Deformable Templates SIAM Journal on Mathematical Analysis. ,vol. 37, pp. 17- 59 ,(2005) , 10.1137/S0036141002404838