$\ell_1$DecNet+: A new architecture framework by $\ell_1$ decomposition and iteration unfolding for sparse feature segmentation

TL;DR

This paper introduces $ _1$DecNet+, a novel architecture combining $ _1$ decomposition with iteration unfolding, to improve sparse feature segmentation by integrating mathematical priors with data-driven methods, demonstrating superior performance in medical and industrial applications.

Contribution

The paper presents $ _1$DecNet+ as the first to incorporate mathematical image priors into segmentation networks, enhancing sparse feature extraction and segmentation performance.

Findings

Achieves equal or better segmentation accuracy than larger models.

Effective in medical and industrial sparse segmentation tasks.

Supports extension to 3D data.

Abstract

$\ell_1$ based sparse regularization plays a central role in compressive sensing and image processing. In this paper, we propose $\ell_1$DecNet, as an unfolded network derived from a variational decomposition model incorporating $\ell_1$ related sparse regularization and solved by scaled alternating direction method of multipliers (ADMM). $\ell_1$DecNet effectively decomposes an input image into a sparse feature and a learned dense feature, and thus helps the subsequent sparse feature related operations. Based on this, we develop $\ell_1$DecNet+, a learnable architecture framework consisting of our $\ell_1$DecNet and a segmentation module which operates over extracted sparse features instead of original images. This architecture combines well the benefits of mathematical modeling and data-driven approaches. To our best knowledge, this is the first study to incorporate mathematical image prior into feature extraction in segmentation network structures. Moreover, our $\ell_1$DecNet+ framework can be easily extended to 3D case. We evaluate the effectiveness of $\ell_1$DecNet+ on two commonly encountered sparse segmentation tasks: retinal vessel segmentation in medical image processing and pavement crack detection in industrial abnormality identification. Experimental results on different datasets demonstrate that, our $\ell_1$DecNet+ architecture with various lightweight segmentation modules can achieve equal or better performance than their enlarged versions respectively. This leads to especially practical advantages on resource-limited devices.