Notes on the Wiener Filter ( “ opti - mal linear filter ” )

To make things less abstract, this can be interpreted as a model for pixels in an image (d), which has been taken by a camera which blurs the light sources (f) via some point spread function (R) and is noisy (n). Note that the light sources are expected to have correlational structure in the real world and the prior over light sources reflects this (Ψ). Particular methods for specifying Ψ are Gaussian processes and Kalman filters (generally in temporal settings). The model reduces to regular factor analysis when Ψ = I, but this choice of prior covariance is just a convention. Imagine we are given some data d and that we know the parameters of the model: What is the posterior distribution over the latent factors, f?