2d spatial convolution sparsenet!

This program is not the fastest implementation of a 2d convolution generative model -- I'm sure you can get significant speed ups using FFTs to do the convolution.

The main point of this program is to allow exploration of the idea of hand- coding invariances. That is, to make it easy to include additional re-mapping matrices that copy each underlying phi basis function to a different size, position, rotation, etc. in a larger image. The only remapping function I have included here is translation, but the code is written in such a way that others can easily be added.

(Well, maybe not so easily at the moment, because it is a bit difficult to understand reinit.m -- sorry about that! I hope to simplify and document that better in the future.)

Also, the code is written in a way that reduces inference back to a standard L2+L1 form. A number of specialized solvers for this problem are available, so it's fun to try them out. Many of them do NOT work well at all in this case, which is highly over-complete and with many of the basis elements tightly packed together.

The remapping matrices are computed by reinit.m and then saved in the cache directory. The first time you run a model of a particular size, the cache will not exist and unittest.m will dump you back at the matlab prompt, where you need to type "reinit" -- this will generate the cache files and save you some computation next time you run the same sized model.

The type of remapping operation implemented in this program is also known as "homogeneous field". I have also extended this code to do "inhomogeneous field" (where different basis elements are copied to different locations), and "repeated inhomogeneous field". If there is any interest in these extensions I would be happy to release them.

--bjc 2011-03-09