The property that wavelets provide sparse representations of images is exploited in many algorithms for image reconstruction from incomplete or noisy data. We like to view this sparsity as a manifestation of the fact that statistics of images are not gaussian. The goal of this project is to investigate and quantify the non-gaussian character of natural or biomedical images. A crucial question is whether or not our recently-constructed sparsity model gives good predictions on the statistical behavior of wavelets coefficients of images and is rich enough to explain the type of dependencies observed in real images. The ultimate goal is to define a parametric statistical model that can be matched to simulations and used as a practical image prior. This also requires the development of corresponding statistical estimators.
Relevant readings:
http://bigwww.epfl.ch/publications/unser1102.html
http://www.sparseprocesses.org/sparseprocesses-chap1.pdf