# WTDUN: Wavelet Tree-Structured Sampling and Deep Unfolding Network for Image Compressed Sensing

arXiv: https://arxiv.org/abs/2411.16336 · HTML: https://mlsanity.com/paper/2411.16336/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 62 references that are in the map.
- First posted on arXiv 25 Nov 2024.

## Builds on (most cited first, 22 of 22)

- [AMP-Net: Denoising based Deep Unfolding for Compressive Image Sensing](https://mlsanity.com/paper/2004.10078/) (2020)
- [Learned D-AMP: Principled Neural Network based Compressive Image Recovery](https://mlsanity.com/paper/1704.06625/) (2017)
- [Deep Gaussian Scale Mixture Prior for Spectral Compressive Imaging](https://mlsanity.com/paper/2103.07152/) (2021)
- [A Deep Learning Approach to Structured Signal Recovery](https://mlsanity.com/paper/1508.04065/) (2015)
- [Group-based Sparse Representation for Image Restoration](https://mlsanity.com/paper/1405.3351/) (2014)
- [ISTA-Net++: Flexible Deep Unfolding Network for Compressive Sensing](https://mlsanity.com/paper/2103.11554/) (2021)
- [Memory-Augmented Deep Unfolding Network for Compressive Sensing](https://mlsanity.com/paper/2110.09766/) (2021)
- [COAST: COntrollable Arbitrary-Sampling NeTwork for Compressive Sensing](https://mlsanity.com/paper/2107.07225/) (2021)
- [Multi-Channel Deep Networks for Block-Based Image Compressive Sensing](https://mlsanity.com/paper/1908.11221/) (2019)
- [Dynamic Path-Controllable Deep Unfolding Network for Compressive Sensing](https://mlsanity.com/paper/2306.16060/) (2023)
- [Convolutional Neural Networks for Non-iterative Reconstruction of Compressively Sensed Images](https://mlsanity.com/paper/1708.04669/) (2017)
- [CSformer: Bridging Convolution and Transformer for Compressive Sensing](https://mlsanity.com/paper/2112.15299/) (2021)
- [FSOINet: Feature-Space Optimization-Inspired Network for Image Compressive Sensing](https://mlsanity.com/paper/2204.05503/) (2022)
- [Global Sensing and Measurements Reuse for Image Compressed Sensing](https://mlsanity.com/paper/2206.11629/) (2022)
- [Fully Convolutional Measurement Network for Compressive Sensing Image Reconstruction](https://mlsanity.com/paper/1712.01641/) (2017)
- [Fast Hierarchical Deep Unfolding Network for Image Compressed Sensing](https://mlsanity.com/paper/2208.01827/) (2022)
- [Image Restoration Using Joint Statistical Modeling in Space-Transform Domain](https://mlsanity.com/paper/1405.3173/) (2014)
- [Dynamic Proximal Unrolling Network for Compressive Imaging](https://mlsanity.com/paper/2107.11007/) (2021)
- [D3C2-Net: Dual-Domain Deep Convolutional Coding Network for Compressive Sensing](https://mlsanity.com/paper/2207.13560/) (2022)
- [Adaptive Measurement Network for CS Image Reconstruction](https://mlsanity.com/paper/1710.01244/) (2017)
- [Full Image Recover for Block-Based Compressive Sensing](https://mlsanity.com/paper/1802.00179/) (2018)
- [Multi-Scale Deep Compressive Sensing Network](https://mlsanity.com/paper/1809.05717/) (2018)

## Abstract (arXiv)

Deep unfolding networks have gained increasing attention in the field of compressed sensing (CS) owing to their theoretical interpretability and superior reconstruction performance. However, most existing deep unfolding methods often face the following issues: 1) they learn directly from single-channel images, leading to a simple feature representation that does not fully capture complex features; and 2) they treat various image components uniformly, ignoring the characteristics of different components. To address these issues, we propose a novel wavelet-domain deep unfolding framework named WTDUN, which operates directly on the multi-scale wavelet subbands. Our method utilizes the intrinsic sparsity and multi-scale structure of wavelet coefficients to achieve a tree-structured sampling and reconstruction, effectively capturing and highlighting the most important features within images. Specifically, the design of tree-structured reconstruction aims to capture the inter-dependencies among the multi-scale subbands, enabling the identification of both fine and coarse features, which can lead to a marked improvement in reconstruction quality. Furthermore, a wavelet domain adaptive sampling method is proposed to greatly improve the sampling capability, which is realized by assigning measurements to each wavelet subband based on its importance. Unlike pure deep learning methods that treat all components uniformly, our method introduces a targeted focus on important subbands, considering their energy and sparsity. This targeted strategy lets us capture key information more efficiently while discarding less important information, resulting in a more effective and detailed reconstruction. Extensive experimental results on various datasets validate the superior performance of our proposed method.