$\ell_1$DecNet+: A new architecture framework by $\ell_1$ decomposition and iteration unfolding for sparse feature segmentation
This work addresses sparse segmentation problems in medical and industrial imaging, presenting a novel integration of mathematical priors into deep learning, though it is incremental as it builds on existing $\ell_1$ and ADMM methods.
The paper tackles sparse feature segmentation by proposing $\ell_1$DecNet+, a framework that decomposes images into sparse and dense features using an unfolded network based on $\ell_1$ regularization and ADMM, then segments the sparse features. It achieves equal or better performance than enlarged segmentation modules on tasks like retinal vessel segmentation and pavement crack detection, offering practical advantages for resource-limited devices.
$\ell_1$ 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.