Convolutional Sparse Coding: Boundary Handling Revisited

TL;DR

This paper critically examines recent boundary handling methods in convolutional sparse coding, identifies their limitations, proposes a solution, and demonstrates its effectiveness in image deblurring tasks.

Contribution

It reveals the failure modes of existing boundary handling approaches and introduces a new method that effectively mitigates boundary artifacts in convolutional sparse coding.

Findings

Existing methods can fail to prevent boundary artifacts under certain conditions

The proposed solution improves boundary artifact mitigation in practice

Application to image deblurring shows practical benefits

Abstract

Two different approaches have recently been proposed for boundary handling in convolutional sparse representations, avoiding potential boundary artifacts arising from the circular boundary conditions implied by the use of frequency domain solution methods by introducing a spatial mask into the convolutional sparse coding problem. In the present paper we show that, under certain circumstances, these methods fail in their design goal of avoiding boundary artifacts. The reasons for this failure are discussed, a solution is proposed, and the practical implications are illustrated in an image deblurring problem.