# American Institute of Mathematical Sciences

November  2009, 3(4): 693-710. doi: 10.3934/ipi.2009.3.693

## Multiscale image representation using novel integro-differential equations

 1 Department of Mathematics, Institute for Physical Science & Technology and Center of Scientific Computation and Mathematical Modeling (CSCAMM), University of Maryland, College Park, MD 20742 2 Applied Mathematics and Scientific Computation (AMSC) and Center of Scientific Computation and Mathematical Modeling (CSCAMM), University of Maryland, College Park, MD 20742, United States

Received  July 2009 Revised  August 2009 Published  October 2009

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 motivation 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.
Citation: Eitan Tadmor, Prashant Athavale. Multiscale image representation using novel integro-differential equations. Inverse Problems and Imaging, 2009, 3 (4) : 693-710. doi: 10.3934/ipi.2009.3.693
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