Image restoration is among other topics such as optical flow, segmentation, inpainting, one of the classical inverse problems in image analysis. The inverse problem consists in recovering information about the original image from incomplete or degraded data. A general principle for dealing with the instability of the inverse problem is that of regularization. A strong relation between a regularization approach and a diffusion process exists via the Euler -Lagrange
equation for the regularization functional. This leads to a scale-space interpretation for linear and non linear regularization.
Here we focus on the development of effective re-usable mathematical software for numerical solution of basic computational kernels for edge-preserving regularization methods. We will describe the computational efforts towards the development an integrated software environment, based on the PETSc (Portable Extensible Toolkit for Scientific computation) parallel virtual machine, for image reconstructions. Application in image inpainting will be described.
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