Exponential decay of scattering coefficients

Abstract : 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).
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Submitted on : Thursday, January 4, 2018 - 12:12:37 PM
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Irène Waldspurger. Exponential decay of scattering coefficients. SampTA 2017 - Sampling Theory and Applications, Jul 2017, Tallinn, Estonia. ⟨hal-01645078v2⟩

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