Integro-Differential Equations Based on (BV, L-1) Image Decomposition
A novel approach for multiscale image processing based on integro-differential equations (IDEs) was proposed in [E. Tadmor and P. Athavale, Inverse Probl. Imaging, 3 (2009), pp. 693-710]. These IDEs, which stem naturally from multiscale (BV, L-2) hierarchical decompositions, yield inverse scale representations of images in the sense that the BV-dual norms of their residuals are inversely proportional to the scaling parameters. Motivated by the fact that (BV, L-1) decomposition is more suitable for extracting local scale-space features than (BV, L-2), we introduce here the IDEs which arise from multiscale (BV, L-1) hierarchical decompositions. We study several variants of this (BV, L-1)-based IDE model, depending on modifications to the curvature term.
integro-differential equation inverse scale hierarchical image decompositions total variation denoising deblurring variational problem energy decomposition