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Universal admissibility for scattering transforms
Max Getter
We resolve the admissibility problem for scattering transforms: every Parseval filter bank on whose low-pass filter is nonvanishing at the origin induces a norm-pres…
The stability landscape in wave-packet scattering: geometric rigidity and sharp Sobolev thresholds
Max Getter, S. Ivan Trapasso
A central problem in harmonic analysis is to understand how frequency resolution constrains stability under nonlinear changes of coordinates. Motivated by Mallat's wavelet scatteri…
Cheeger Bounds for Stable Phase Retrieval in Reproducing Kernel Hilbert Spaces
Hartmut Führ, Max Getter
Phase retrieval seeks to reconstruct a signal from phaseless intensity measurements and, in applications where measurements contain errors, demands stable reconstruction. We study…
Energy Propagation in Scattering Convolution Networks Can Be Arbitrarily Slow
Hartmut Führ, Max Getter
We analyze energy decay for deep convolutional neural networks employed as feature extractors, including Mallat's wavelet scattering transform. For time-frequency scattering transf…