Exponential decay of scattering coefficients
Waldspurger, Irène (2017), Exponential decay of scattering coefficients, 2017 International Conference on Sampling Theory and Applications (SampTA), IEEE, p. 143-146. 10.1109/SAMPTA.2017.8024473
TypeCommunication / Conférence
Conference titleSampTA 2017 - Sampling Theory and Applications, 3-7 juillet 2017, Tallinn, Estonia
Book title2017 International Conference on Sampling Theory and Applications (SampTA)
MetadataShow full item record
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)The scattering transform is a deep representation, defined as a cascade of wavelet transforms followed by the application of a complex modulus. In her PhD, the author showed that, under some conditions on the wavelets, the norm of the scattering coefficients at a given layer only depends on the values of the signal outside a frequency band whose size is exponential in the depth of the layer. We give here a succinct presentation of this result, and slightly generalize it by removing one of the assumptions on the wavelets (namely the weak analyticity condition).
Subjects / KeywordsScattering; Wavelet transforms; exponential decay
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