PNNL

Abstract

We augment orthogonal matching pursuit (OMP) by introducing an additional step in the identification stage of each pursuit iteration. At each iteration a “path,” or geodesic, is generated between the two dictionary atoms that are most correlated with the residual and from this path select a new atom that has a greater correlation to the residual than either of the two bracketing atoms. Two methods of constructing a path are investigated: the Euclidean geodesic formed by a linear combination of the two atoms and the 2-Wasserstein geodesic corresponding to the optimal transport map between the atoms. The existence of a higher-correlation atom is proven in the Euclidean case under assumptions on the two bracketing atoms. In addition, we provide computational results illustrating improvements in sparse coding and denoising relative to baseline OMP. Although we demonstrate our augmentation on OMP alone, in general it may be applied to any reconstruction algorithm that relies on the selection and sorting of high-similarity atoms during an analysis or identification phase.