# ℓ1DecNet+: A new architecture framework by ℓ1 decomposition and iteration unfolding for sparse feature segmentation

arXiv: https://arxiv.org/abs/2203.02690 · HTML: https://mlsanity.com/paper/2203.02690/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 71 references that are in the map.
- First posted on arXiv 5 Mar 2022.

## Builds on (most cited first, 17 of 17)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [EfficientNet: Rethinking Model Scaling for Convolutional Neural Networks](https://mlsanity.com/paper/1905.11946/) (2019)
- [SegFormer: Simple and Efficient Design for Semantic Segmentation with Transformers](https://mlsanity.com/paper/2105.15203/) (2021)
- [Multi-Scale Context Aggregation by Dilated Convolutions](https://mlsanity.com/paper/1511.07122/) (2015)
- [Deep Equilibrium Models](https://mlsanity.com/paper/1909.01377/) (2019)
- [UNet++: Redesigning Skip Connections to Exploit Multiscale Features in Image Segmentation](https://mlsanity.com/paper/1912.05074/) (2019)
- [Stable Architectures for Deep Neural Networks](https://mlsanity.com/paper/1705.03341/) (2017)
- [Deep Unfolding Network for Image Super-Resolution](https://mlsanity.com/paper/2003.10428/) (2020)
- [Learned Primal-dual Reconstruction](https://mlsanity.com/paper/1707.06474/) (2017)
- [PDE-Net 2.0: Learning PDEs from Data with A Numeric-Symbolic Hybrid Deep Network](https://mlsanity.com/paper/1812.04426/) (2018)
- [Trainable Nonlinear Reaction Diffusion: A Flexible Framework for Fast and Effective Image Restoration](https://mlsanity.com/paper/1508.02848/) (2015)
- [FISTA-Net: Learning A Fast Iterative Shrinkage Thresholding Network for Inverse Problems in Imaging](https://mlsanity.com/paper/2008.02683/) (2020)
- [AMP-Net: Denoising based Deep Unfolding for Compressive Image Sensing](https://mlsanity.com/paper/2004.10078/) (2020)
- [Memory-Augmented Deep Unfolding Network for Compressive Sensing](https://mlsanity.com/paper/2110.09766/) (2021)
- [Infimal convolution of data discrepancies for mixed noise removal](https://mlsanity.com/paper/1611.00690/) (2016)
- [Effective two-stage image segmentation: a new non-Lipschitz decomposition approach with convergent algorithm](https://mlsanity.com/paper/2009.06177/) (2020)

## Built on by (most cited first, 3 of 3)

- [A better approach to diagnose retinal diseases: Combining our Segmentation-based Vascular Enhancement with deep learning features](https://mlsanity.com/paper/2405.16235/) (2024)
- [Robust Variational Model Based Tailored UNet: Leveraging Edge Detector and Mean Curvature for Improved Image Segmentation](https://mlsanity.com/paper/2512.07590/) (2025)
- [LHMCF-Net: A Learned Hyperbolic Mean Curvature Flow Network for Medical Images Segmentation](https://mlsanity.com/paper/2608.20942/) (2026)

## Abstract (arXiv)

ℓ1 based sparse regularization plays a central role in compressive sensing and image processing. In this paper, we propose ℓ1DecNet, as an unfolded network derived from a variational decomposition model incorporating ℓ1 related sparse regularization and solved by scaled alternating direction method of multipliers (ADMM). ℓ1DecNet 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 ℓ1DecNet+, a learnable architecture framework consisting of our ℓ1DecNet 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 ℓ1DecNet+ framework can be easily extended to 3D case. We evaluate the effectiveness of ℓ1DecNet+ 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 ℓ1DecNet+ 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.