An improved theoretical analysis of convolutional sparse coding using stripe coherence

Abstract

Convolutional sparse coding has proven to be very effective in a wide range of applications. Recent work addressed the theoretical performance of global orthogonal matching pursuit (OMP) using the stripe coherence that is a stronger characterization of the convolutional dictionary. In this paper, we further provide the theoretical analysis of convolutional sparse model. Our result improves the guarantee condition for global OMP based on convolutional sparse model. We also provide the theoretical guarantee for basis pursuit using stripe coherence based on convolutional sparse model, which is absent in the existing results.