In original FRAME, "learning filters" means selecting filters from a (very small) fixed set. In this paper they add* an additional "bilevel optimization", where they both learn θ_j, the parameters of the filters, and select the filters (indicator variables z_j).

Either way, that learning is the entropy minimisation part.

Maximizing entropy is not really about learning anything, it's about not overfitting. (Although you are correct in that you have to find the Langrange multipliers to correctly combine the filters.) Basically, the desired probability distribution will be constrained only by certain statistics of (the filters you learnt) on the data, and nothing else. For example, you want a model that says "if panel 1 has an N-sided polygon, and panel 2 has an N+1-sided polygon, panel 3 has an N+2-sided polygon", and says nothing about anything else.

* I'm a bit peeved they didn't cite me for extending FRAME by learning the features like that. That was my PhD topic. But let's face it, they probably don't know about my work, or quickly forgot it because the papers were too ugly, and admittedly they've done it in a cleaner way. I had to wrap kludgy iterative feature addition around the feature optimisation step to make it more efficient for image modelling.