  Deconvolution is a fundamental inverse problem in signal processing and the
prototypical model for recovering a signal from its noisy measurement.
Nevertheless, the majority of model-based inversion techniques require
knowledge on the convolution kernel to recover an accurate reconstruction and
additionally prior assumptions on the regularity of the signal are needed. To
overcome these limitations, we parametrise the convolution kernel and prior
length-scales, which are then jointly estimated in the inversion procedure. The
proposed framework of blind hierarchical deconvolution enables accurate
reconstructions of functions with varying regularity and unknown kernel size
and can be solved efficiently with an empirical Bayes two-step procedure, where
hyperparameters are first estimated by optimisation and other unknowns then by
an analytical formula.
