  Ill-posed inverse problems are commonplace in biomedical image processing.
Their solution typically requires imposing prior knowledge about the latent
ground truth. While this regularizes the problem to an extent where it can be
solved, it also biases the result toward the expected. With inappropriate
priors harming more than they use, it remains unclear what prior to use for a
given practical problem. Priors are hence mostly chosen in an {\em ad hoc} or
empirical fashion. We argue here that the gradient distribution of
natural-scene images may provide a versatile and well-founded prior for
biomedical images. We provide motivation for this choice from different points
of view, and we fully validate the resulting prior for use on biomedical images
by showing its stability and correlation with image quality. We then provide a
set of simple parametric models for the resulting prior, leading to
straightforward (quasi-)convex optimization problems for which we provide
efficient solver algorithms. We illustrate the use of the present models and
solvers in a variety of common image-processing tasks, including contrast
enhancement, noise level estimation, denoising, blind deconvolution,
zooming/up-sampling, and dehazing. In all cases we show that the present method
leads to results that are comparable to or better than the state of the art;
always using the same, simple prior. We conclude by discussing the limitations
and possible interpretations of the prior.

Computer Vision and Pattern Recognition