Journal
IEEE TRANSACTIONS ON IMAGE PROCESSING
Volume 24, Issue 6, Pages 1777-1790Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TIP.2015.2409562
Keywords
Image denosing; image enhancement; image reconstruction
Funding
- Air Force Office of Scientific Research, Air Force Office of Scientific Research, Arlington, VA [FA9550-12-1-0364]
- Office of Naval Research, Arlington, VA, USA
- Schweizerische Nationalfonds zur Forderung der Wissenschaftlichen Forschung [P2ELP2_148890]
- Swiss National Science Foundation (SNF) [P2ELP2_148890] Funding Source: Swiss National Science Foundation (SNF)
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Natural images exhibit geometric structures that are informative of the properties of the underlying scene. Modern image processing algorithms respect such characteristics by employing regularizers that capture the statistics of natural images. For instance, total variation (TV) respects the highly kurtotic distribution of the pointwise gradient by allowing for large magnitude outlayers. However, the gradient magnitude alone does not capture the directionality and scale of local structures in natural images. The structure tensor provides a more meaningful description of gradient information as it describes both the size and orientation of the image gradients in a neighborhood of each point. Based on this observation, we propose a variational model for image reconstruction that employs a regularization functional adapted to the local geometry of image by means of its structure tensor. Our method alternates two minimization steps: 1) robust estimation of the structure tensor as a semidefinite program and 2) reconstruction of the image with an adaptive regularizer defined from this tensor. This two-step procedure allows us to extend anisotropic diffusion into the convex setting and develop robust, efficient, and easy-to-code algorithms for image denoising, deblurring, and compressed sensing. Our method extends naturally to nonlocal regularization, where it exploits the local self-similarity of natural images to improve nonlocal TV and diffusion operators. Our experiments show a consistent accuracy improvement over classic regularization.
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