Quadtree structured restoration algorithms for piecewise polynomial images

Iterative shrinkage of sparse and redundant representations are at the heart of many state of the art denoising and deconvolution algorithms. They assume the signal is well approximated by a few elements from an overcomplete basis of a linear space. If one instead selects the elements from a nonlinear manifold it is possible to more efficiently represent piecewise polynomial signals. This suggests that image restoration algorithms based around nonlinear transformations could provide better results for this class of signals. This paper uses iterative shrinkage ideas and a nonlinear quadtree decomposition to develop image restoration algorithms suitable for piecewise polynomial images.