Inducing wavelets into random fields via generative boosting

This paper proposes a learning algorithm for the random field models whose energy functions are in the form of linear combinations of rectified filter responses from subsets of wavelets selected from a given over-complete dictionary. The algorithm consists of the following two components. (1) We propose to induce the wavelets into the random field model by a generative version of the epsilon-boosting algorithm. (2) We propose to generate the synthesized images from the random field model using Gibbs sampling on the coefficients (or responses) of the selected wavelets. We show that the proposed learning and sampling algorithms are capable of generating realistic image patterns. We also evaluate our learning method on a dataset of clustering tasks to demonstrate that the models can be learned in an unsupervised setting. The learned models encode the patterns in wavelet sparse coding. Moreover, they can be mapped to the second-layer nodes of a sparsely connected convolutional neural network (CNN).