Inverse Problems with Invariant Multiscale Statistics

18 Sep 2016  ·  Ivan Dokmanić, Joan Bruna, Stéphane Mallat, Maarten de Hoop ·

We propose a new approach to linear ill-posed inverse problems. Our algorithm alternates between enforcing two constraints: the measurements and the statistical correlation structure in some transformed space. We use a non-linear multiscale scattering transform which discards the phase and thus exposes strong spectral correlations otherwise hidden beneath the phase fluctuations. As a result, both constraints may be put into effect by linear projections in their respective spaces. We apply the algorithm to super-resolution and tomography and show that it outperforms ad hoc convex regularizers and stably recovers the missing spectrum.

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Computational Engineering, Finance, and Science


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