Deformation-invariant sparse coding

Abstract

Sparse coding represents input signals each as a sparse linear combination of a set of basis or dictionary elements where sparsity encourages representing each input signal with a few of the most indicative dictionary elements. In this thesis, we extend sparse coding to allow dictionary elements to undergo deformations, resulting in a general probabilistic model and accompanying inference algorithm for estimating sparse linear combination weights, dictionary elements, and deformations. We apply our proposed method on functional magnetic resonance imaging (fMRI) data, where the locations of functional regions in the brain evoked by a specific cognitive task may vary across individuals relative to anatomy. For a language fMRI study, our method identifies activation regions that agree with known literature on language processing. Furthermore, the deformations learned by our inference algorithm produce more robust group-level effects than anatomical alignment alone.