Integro-Differential Equations Based on (BV, L1) 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) 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) decomposition is more suitable for extracting local scale-space features than (BV,L), we introduce here the IDEs which arise from multiscale (BV,L) hierarchical decompositions. We study several variants of this (BV,L)-based IDE model, depending on modifications to the curvature term.