Bayesian Interpretation of Inverse Problems


In literature, many works mention the relationship between inverse problems and their Bayesian interpretation. Although it is straightforward to derive this relationship, I haven't seen any work that explain this explicitly. This blogpost can be seen as a simple tutorial introduction to the Bayesian view of the inverse problems. In the following section, we take only a simple denoising problem as an inverse problem and show its probabilistic interpretation. Then, we show how to incorporate the prior into the model. Then in a separate section, we explain well-known inverse problems with connections to time-frequency analysis and matrix factorisations.