Path Orthogonal Matching Pursuit for Sparse Reconstruction and Denoising of SWIR Maritime Imagery

Abstract

We introduce an extension that may be used to augment algorithms used for the sparse decomposition of signals into a linear combination of atoms drawn from a dictionary such as those used in support of, for example, compressive sensing, k-sparse representation, and denoising. Our augmentation may be applied to any reconstruction algorithm that relies on the selection and sorting of high-correlation atoms during an analysis or identification phase by generating a "path" between the two highest-correlation atoms. Here we investigate two types of path: a linear combination (Euclidean geodesic) and a construction relying on an optimal transport map (2-Wasserstein geodesic). We test our extension by performing image denoising and k-sparse representation using atoms from a learned overcomplete kSVD dictionary. We study the application of our techniques on SWIR imagery of maritime vessels and show that our methods outperform orthogonal matching pursuit. We conclude that these methods, having shown success in our two tested problem domains, will also be useful for reducing "basis mismatch" error that arises in the recovery of compressively sampled images.