  Compressive sensing (CS) reconstructs images from sub-Nyquist measurements by
solving a sparsity-regularized inverse problem. Traditional CS solvers use
iterative optimizers with hand crafted sparsifiers, while early data-driven
methods directly learn an inverse mapping from the low-dimensional measurement
space to the original image space. The latter outperforms the former, but is
restrictive to a pre-defined measurement domain. More recent, deep unrolling
methods combine traditional proximal gradient methods and data-driven
approaches to iteratively refine an image approximation. To achieve higher
accuracy, it has also been suggested to learn both the sampling matrix, and the
choice of measurement vectors adaptively. Contrary to the current trend, in
this work we hypothesize that a general inverse mapping from a random set of
compressed measurements to the image domain exists for a given measurement
basis, and can be learned. Such a model is single-shot, non-restrictive and
does not parametrize the sampling process. To this end, we propose MOSAIC, a
novel compressive sensing framework to reconstruct images given any random
selection of measurements, sampled using a fixed basis. Motivated by the uneven
distribution of information across measurements, MOSAIC incorporates an
embedding technique to efficiently apply attention mechanisms on an encoded
sequence of measurements, while dispensing the need to use unrolled deep
networks. A range of experiments validate our proposed architecture as a
promising alternative for existing CS reconstruction methods, by achieving the
state-of-the-art for metrics of reconstruction accuracy on standard datasets.
