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.

Source: http://lslink.info/?c=2M