Image restoration using a sparse quadtree decomposition representation

Techniques based on sparse and redundant representations are at the heart of many state of the art denoising and deconvolution algorithms. A very sparse representation of piecewise polynomial images can be obtained by using a quadtree decomposition to adaptively select a basis. We have recently exploited this to restore images of this form, however the same model can also provide very good sparse approximations of real world images. In this paper we take advantage of this to develop both image denoising and deconvolution algorithms suitable for real world images. We present results on the cameraman image showing comparable performance with iterative soft thresholding using the undecimated wavelet transform.