Convolutional Trees for Fast Transform Learning

Abstract—Dictionary learning is a powerful approach for sparse representation. However, the numerical complexity of classical dictionary learning methods restricts their use to atoms with small supports such as patches. In a previous work, we introduced a model based on a composition of convolutions with sparse kernels to build large dictionary atoms with a low computational cost. The subject of this work is to consider this model at the next level, i.e., to build a full dictionary of atoms from convolutions of sparse kernels. Moreover, we further reduce the size of the representation space by organizing the convolution kernels used to build atoms into a tree structure. The performance of the method is tested for the construction of a curvelet dictionary with a known code. I