Inverse Problems with Invariant Multiscale Statistics
By Ivan Dokmanić, Joan Bruna, Stéphane Mallat, Maarten V. de Hoop. 2016
12 citations recorded by the source corpus.
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.
Subfields: Computational Mechanics, Computer Vision and Pattern Recognition, Mathematical Physics, Numerical Methods & Scientific Computing
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Computational Mechanics
- Matthew B. Blaschko
- Simon Lacoste-Julien
- Eugene Belilovsky
- Nikos Komodakis
- Edouard Oyallon
- Peter Richtárik
- Francis R. Bach
- Suvrit Sra
In Computer Vision and Pattern Recognition
- Andrea Vedaldi
- Luc Van Gool
- Andrew Zisserman
- Dacheng Tao
- Xiaogang Wang
- Cordelia Schmid
- Trevor Darrell
- Jitendra Malik
In Mathematical Physics
In Numerical Methods & Scientific Computing
Citations in the corpus
- Scattering Networks for Hybrid Representation Learning (2018, background): “This representation has been proved to linearize small deformations of images [35], be non-expansive and almost complete [10], [17], which makes it an ideal input to a deep network algorithm, which can build invariants to this local variability via a first linear operator.”
- Learned Primal-Dual Reconstruction (2017, unknown): “wavelet transforms (scattering transform) [11].”