Bayesian estimation

Bayesian estimation theory is a general tool for estimating the parameters of a source distribution given: (a) the transfer function between source and observation; (b) observations of the system, and estimates of the noise on those observations; and (c) some prior probability distribution for the parameter values.

Bayesian analysis yields both the parameter values and an estimate of the errors on the values. The evidence provides a quantitative estimate of the probability attached to a particular set of values, which thus allows direct comparison between different feasible solutions.

There is a huge variety of applications for such a methodology. One of the best-known is the area of image processing, where we want to estimate the pixel values of the true, or underlying, image, given only some observed data which have been convolved with some instrumental point spread function (PSF).

Bayesian estimation procedures are described in more detail in the references.

Image processing ...

Image deconvolution

Some blurred text from "Hamlet" before (above) and after (below) deconvolution with MemSys. (Click on images to see full size)

More examples...