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Researcher: Hanne Kekkonen

In this project we examine sparsity promoting alternatives for Bayesian a priori distributions that are frequently used in study of inverse problems. The aim is to construct priors that have the same kind of good edge-preserving properties as total variation or Mumford-Shah but correspond to well-defined infinite dimensional random variables and can be approximated with finite dimensional random variables. Our approach is to introducing a new 'wavelet tree' random variable, which acts as a nonlinear activation function choosing only the wavelet branches that are deemed useful.