Abstract
ABSTRACT Motivated by the hierarchical multiscale image representation of Tadmor et al., 1 we propose a novel integro-dierential equation (IDE) for a multiscale image representation. To this end, one integrates in inverse scale spacea succession of rened, recursive slices of the image, which are balanced by a typical curvature term at the nerscale. Although the original motivation came from a variational approach, the resulting IDE can be extendedusing standard techniques from PDE-based image processing. We use ltering, edge preserving smoothing toyield a family of modied IDE models with applications to image denoising and image deblurring problems. TheIDE 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. Finally, wealso propose another novel IDE based on the ( BV,L 1 ) decomposition. We present numerical results for this IDEand its variant and examine its properties.Keywords: natural images, multiscale representation, total variation, denoising, deblurring, inverse scale, vari-ational problem, integro -dierential equation , energy decomposition.
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