Convolutional Sparse Coding with Multipath Orthogonal Matching Pursuit

Abstract

Finding patterns in time series is crucial to understanding physical or physiological phenomena monitored with sensors. Convolutional sparse coding (CSC) methods, which approximate signals by a sparse combination of short signal templates (also called atoms), are well-suited for this task. Nevertheless, sparsity results in intractable non-convex optimization problems. This paper introduces an algorithm, based on Multi-path Matching Pursuit, which is novel in convolutional settings, to efficiently and accurately estimate atoms’ localizations in time series. We describe a principled way to improve this greedy procedure by returning several candidate solutions instead of one. Our approach yields better localization and signal reconstruction on simulated data and in a real-world use case, which consists in automatically detect damages, such as cracks and broken wires, in overhead power lines.