Filter interpretation of regularized impulse response modeling

In this work, we look at Bayesian regularization for FIR modeling from a different angle. Instead of focusing directly on the kernel matrix, and on how the information about the covariance of the parameters is encoded in such a matrix, we address its inverse, the regularization matrix, and we look more closely at how the parameters are penalized in the cost function. This approach allows one to embed prior knowledge directly in the regularization term, as a prefiltering of the model parameters. In this framework, new regularization structures can be designed, giving the user the freedom to adapt the problem formulation to his/her specifications.