Sparsity-promoting Bayesian inversion

A computational Bayesian inversion model is demonstrated. It is discretization invariant, describes prior information using function spaces with a wavelet basis and promotes reconstructions that are sparse in the wavelet transform domain. The method makes use of the Besov space prior with p = 1, q = 1 and s = 1, which is related to the total variation prior. Numerical evidence is presented in the context of a one-dimensional deconvolution task, suggesting that edge-preserving and noise-robust reconstructions can be achieved consistently at various resolutions.