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Abstract:
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Scattering networks are Convolutional Networks where the convolutional filter banks are given by complex, multiresolution wavelet families. As a result of this extra structure, they are provably stable and locally invariant signal representations, and yield state-of-the-art classification results on several pattern and texture recognition problems where training examples may be limited. The reasons for such success lie on the ability to preserve discriminative information while generating stability with respect to high-dimensional deformations.
In this talk, we will explore the discriminative aspect of the representation, giving conditions under which signals can be recovered from their scattering coefficients, as well as introducing a family of Gibbs scattering processes, from which one can sample image and auditory textures. Although the scattering recovery is non-convex and corresponds to a generalized phase recovery problem, gradient descent algorithms show good empirical performance and enjoy weak convergence properties. We will discuss connections with non-linear compressed sensing and applications to texture synthesis and inverse problems such as super-resolution.
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