  Inverse problems play a key role in modern image/signal processing methods.
However, since they are generally ill-conditioned or ill-posed due to lack of
observations, their solutions may have significant intrinsic uncertainty.
Analysing and quantifying this uncertainty is very challenging, particularly in
high-dimensional problems and problems with non-smooth objective functionals
(e.g. sparsity-promoting priors). In this article, a series of strategies to
visualise this uncertainty are presented, e.g. highest posterior density
credible regions, and local credible intervals (cf. error bars) for individual
pixels and superpixels. Our methods support non-smooth priors for inverse
problems and can be scaled to high-dimensional settings. Moreover, we present
strategies to automatically set regularisation parameters so that the proposed
uncertainty quantification (UQ) strategies become much easier to use. Also,
different kinds of dictionaries (complete and over-complete) are used to
represent the image/signal and their performance in the proposed UQ methodology
is investigated.
