${\mathcal{l}}_{1}$ DecNet+: A New Architecture Framework by ${\mathcal{l}}_{1}$ Decomposition and Iteration Unfolding for Sparse Feature Segmentation

Abstract

${\mathcal{l}}_{1}$ based sparse regularization plays a central role in compressive sensing and image processing. In this paper, we propose ${\mathcal{l}}_{1}$ DecNet, as an unfolded network derived from a variational decomposition model, which incorporates ${\mathcal{l}}_{1}$ related sparse regularizations and is solved by a non-standard scaled alternating direction method of multipliers. ${\mathcal{l}}_{1}$ DecNet effectively separates a spatially sparse feature and a learned spatially dense feature from an input image, and thus helps the subsequent spatially sparse feature related operations. Based on this, we develop ${\mathcal{l}}_{1}$ DecNet+, a learnable architecture framework consisting of our ${\mathcal{l}}_{1}$ 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 ${\mathcal{l}}_{1}$ DecNet + framework can be easily extended to 3D case. We evaluate the effectiveness of ${\mathcal{l}}_{1}$ 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 ${\mathcal{l}}_{1}$ 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.

Keywords

Variational model / ${\mathcal{l}}_{1}$ regularization / ${\mathcal{l}}_{1}$ decomposition / ADMM / deep unfolding / sparse feature extraction / sparse feature segmentation