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Enhanced compressed sensing recovery with level set normals.

Authors
  • Estellers, Virginia
  • Thiran, Jean-Philippe
  • Bresson, Xavier
Type
Published Article
Journal
IEEE Transactions on Image Processing
Publisher
Institute of Electrical and Electronics Engineers
Publication Date
Jul 01, 2013
Volume
22
Issue
7
Pages
2611–2626
Identifiers
DOI: 10.1109/TIP.2013.2253484
PMID: 23529094
Source
Medline
License
Unknown

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 nonlocal operators and graphs to exploit the repetitive nature of textured images 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.

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