I recently discovered two neat papers on deconvolution from a Bayesian perspective, written by Kevin Knuth.
http://knuthlab.rit.albany.edu/papers/knuth-ica99.pdf
Abstract: The problem of source separation is by its very nature an inductive inference problem. There is not enough information to deduce the solution, so one must use any available information to infer the most probable solution. We demonstrate that source separation problems are well-suited for the Bayesian approach which provides a natural and logically consistent method by which one can incorporate prior knowledge to estimate the most probable solution given that knowledge.
We derive the Bell-Sejnowski ICA algorithm from first principles, i.e. Bayes' Theorem and demonstrate how the Bayesian methodology makes explicit the underlying assumptions. We then further demonstrate the power of the Bayesian approach by deriving two separation algorithms that incorporate additional prior information. One algorithm separates signals that are known a priori to be decorrelated and the other utilizes information about the signal propagation through the medium from the sources to the detectors.
http://knuthlab.rit.albany.edu/papers/knuth-eusipco05-final....
Abstract: Source separation problems are ubiquitous in the physical
sciences; any situation where signals are superimposed calls
for source separation to estimate the original signals. In this
tutorial I will discuss the Bayesian approach to the source
separation problem. This approach has a specific advantage
in that it requires the designer to explicitly describe the signal
model in addition to any other information or assumptions
that go into the problem description. This leads naturally to
the idea of informed source separation, where the algorithm
design incorporates relevant information about the specific
problem. This approach promises to enable researchers to
design their own high-quality algorithms that are specifically
tailored to the problem at hand.