Group Invariant Scattering
Group Invariant Scattering
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DOI：
10.1002/cpa.21413
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发表时间：
2012-10-01
影响因子：
3
通讯作者：
Mallat, Stephane
中科院分区：
文献类型：
--
作者：
Mallat, Stephane
本文构造了L-2（R-d）上的线性不变算子，它们对非同态作用是Lipschitz连续的.散射传播算子是非线性算子和非交换算子的路径有序乘积，每个算子计算小波变换的模。局部积分定义了一个加窗散射变换，证明了它对C-2同态的作用是Lipschitz连续的。随着窗口大小的增加，它收敛到平移不变的小波散射变换。散射系数也提供了平稳过程的表示。期望值取决于高阶矩，可以区分具有相同功率谱的过程。在L-2（G）上推广了散射算子，其中G是紧李群，并且在G的作用下是不变的。结合L-2（R-d）和L-2（SO（d））上的散射定义了L-2（R-d）上的平移和旋转不变散射。(c)2012 Wiley Periodicals，Inc.
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 of nonlinear and noncommuting operators, each of which computes the modulus of a wavelet transform. A local integration defines a windowed scattering transform, which is proved to be Lipschitz-continuous to the action of C-2 diffeomorphisms. As the window size increases, it converges to a wavelet scattering transform that is translation invariant. Scattering coefficients also provide representations of stationary processes. Expected values depend upon high-order moments and can discriminate processes having the same power spectrum. Scattering operators are extended on L-2(G), where G is a compact Lie group, and are invariant under the action of G. Combining a scattering on L-2(R-d) and on L-2(SO(d)) defines a translation- and rotation-invariant scattering on L-2(R-d). (c) 2012 Wiley Periodicals, Inc.