Enhanced Compressed Sensing Recovery with Level Set Normals

TL;DR

This paper introduces a novel compressed sensing algorithm that leverages geometric image properties, specifically level set normals, to improve image reconstruction quality from limited measurements, with extensions to non-local operators and graphs.

Contribution

The paper presents a new image reconstruction method using level set normals in compressed sensing, incorporating convex minimization and extending to textured images for enhanced detail recovery.

Findings

Outperforms state-of-the-art algorithms in image quality

Demonstrates robustness to noise and measurement reduction

Efficient convex optimization-based implementation

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.