  We propose a compressive sensing algorithm that exploits geometric properties
of images to recover images of high quality from few measurements. The image
reconstruction is done by iterating the two following steps: 1) estimation of
normal vectors of the image level curves and 2) reconstruction of an image
fitting the normal vectors, the compressed sensing measurements and the
sparsity constraint. The proposed technique can naturally extend to non local
operators and graphs to exploit the repetitive nature of textured images in
order to recover fine detail structures. In both cases, the problem is reduced
to a series of convex minimization problems that can be efficiently solved with
a combination of variable splitting and augmented Lagrangian methods, leading
to fast and easy-to-code algorithms. Extended experiments show a clear
improvement over related state-of-the-art algorithms in the quality of the
reconstructed images and the robustness of the proposed method to noise,
different kind of images and reduced measurements.
