Enhanced Compressed Sensing Recovery with Level Set Normals
This work addresses image reconstruction in compressive sensing, offering incremental improvements for applications requiring efficient data acquisition and recovery.
The paper tackles the problem of recovering high-quality images from few measurements in compressive sensing by exploiting geometric properties of images, resulting in a method that shows clear improvement over state-of-the-art algorithms in reconstruction quality and robustness to noise, different image types, and reduced measurements.
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.