Abstract

We describe a method for fast approximation of sparse coding. A given input vector is passed through a binary tree. Each leaf of the tree contains a subset of dictionary elements. The coefficients corresponding to these dictionary elements are allowed to be nonzero and their values are calculated quickly by multiplication with a precomputed pseudoinverse. The tree parameters, the dic- tionary, and the subsets of the dictionary corresponding to each leaf are learned. In the process of describing this algorithm, we discuss the more general problem of learning the groups in group structured sparse modeling. We show that our method creates good sparse representations by using it in the object recognition the whole system runs at 20 frames per second on 321 ?481 sized images on a framework of [1,2]. Implementing our own fast version of the SIFT descriptor laptop with a quad-core cpu, while sacri ficing very little accuracy on the Caltech 101, Caltech 256, and 15 scenes benchmarks.