Enhanced Compressed Sensing Recovery with Level Set Normals by Virginia Estellers, Jean-Philippe Thiran, Xavier Bresson
Abstract 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.
An implementation for the Enhanced Compressed Sensing Recovery with Level Set Normals can be found here.
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