Multiscale image representation using novel integro-differential equations

Abstract

Motivated by the hierarchical multiscale image representation of Tadmor et. al., (25), we propose a novel integro-differential equation (IDE) for a multiscale image representation. To this end, one integrates in inverse scale space a succession of refined, recursive 'slices' of the image, which are balanced by a typical curvature term at the finer scale. Although the original moti- vation came from a variational approach, the resulting IDE can be extended using standard techniques from PDE-based image processing. We use filtering, edge preserving and tangential smoothing to yield a family of modified IDE models with applications to image denoising and image deblurring problems. The IDE models depend on a user scaling function which is shown to dictate the BV ∗ properties of the residual error. Numerical experiments demonstrate application of the IDE approach to denoising and deblurring.