# D3C2-Net: Dual-Domain Deep Convolutional Coding Network for Compressive Sensing

arXiv: https://arxiv.org/abs/2207.13560 · HTML: https://mlsanity.com/paper/2207.13560/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 89 references that are in the map.
- First posted on arXiv 27 Jul 2022.

## Builds on (most cited first, 25 of 25)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Understanding the Effective Receptive Field in Deep Convolutional Neural Networks](https://mlsanity.com/paper/1701.04128/) (2017)
- [Deep Laplacian Pyramid Networks for Fast and Accurate Super-Resolution](https://mlsanity.com/paper/1704.03915/) (2017)
- [Learning Deep CNN Denoiser Prior for Image Restoration](https://mlsanity.com/paper/1704.03264/) (2017)
- [MoDL: Model Based Deep Learning Architecture for Inverse Problems](https://mlsanity.com/paper/1712.02862/) (2017)
- [A Deep Cascade of Convolutional Neural Networks for Dynamic MR Image Reconstruction](https://mlsanity.com/paper/1704.02422/) (2017)
- [Trainable Nonlinear Reaction Diffusion: A Flexible Framework for Fast and Effective Image Restoration](https://mlsanity.com/paper/1508.02848/) (2015)
- [Scaling Up Your Kernels to 31x31: Revisiting Large Kernel Design in CNNs](https://mlsanity.com/paper/2203.06717/) (2022)
- [A Model-driven Deep Neural Network for Single Image Rain Removal](https://mlsanity.com/paper/2005.01333/) (2020)
- [Deep learning for undersampled MRI reconstruction](https://mlsanity.com/paper/1709.02576/) (2017)
- [Equivariant Imaging: Learning Beyond the Range Space](https://mlsanity.com/paper/2103.14756/) (2021)
- [Deep Convolutional Neural Network for Multi-modal Image Restoration and Fusion](https://mlsanity.com/paper/1910.04066/) (2019)
- [DuDoNet: Dual Domain Network for CT Metal Artifact Reduction](https://mlsanity.com/paper/1907.00273/) (2019)
- [AMP-Net: Denoising based Deep Unfolding for Compressive Image Sensing](https://mlsanity.com/paper/2004.10078/) (2020)
- [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)
- [Dense Deep Unfolding Network with 3D-CNN Prior for Snapshot Compressive Imaging](https://mlsanity.com/paper/2109.06548/) (2021)
- [Learned Convolutional Sparse Coding](https://mlsanity.com/paper/1711.00328/) (2017)
- [Model Learning: Primal Dual Networks for Fast MR imaging](https://mlsanity.com/paper/1908.02426/) (2019)
- [Content-aware Scalable Deep Compressed Sensing](https://mlsanity.com/paper/2207.09313/) (2022)
- [Image Compressive Sensing Recovery Using Adaptively Learned Sparsifying Basis via L0 Minimization](https://mlsanity.com/paper/1404.7566/) (2014)

## Built on by (most cited first, 4 of 4)

- [V2A-Mark: Versatile Deep Visual-Audio Watermarking for Manipulation Localization and Copyright Protection](https://mlsanity.com/paper/2404.16824/) (2024)
- [OmniSSR: Zero-shot Omnidirectional Image Super-Resolution using Stable Diffusion Model](https://mlsanity.com/paper/2404.10312/) (2024)
- [ResVR: Joint Rescaling and Viewport Rendering of Omnidirectional Images](https://mlsanity.com/paper/2404.16825/) (2024)
- [WTDUN: Wavelet Tree-Structured Sampling and Deep Unfolding Network for Image Compressed Sensing](https://mlsanity.com/paper/2411.16336/) (2024)

## Abstract (arXiv)

By mapping iterative optimization algorithms into neural networks (NNs), deep unfolding networks (DUNs) exhibit well-defined and interpretable structures and achieve remarkable success in the field of compressive sensing (CS). However, most existing DUNs solely rely on the image-domain unfolding, which restricts the information transmission capacity and reconstruction flexibility, leading to their loss of image details and unsatisfactory performance. To overcome these limitations, this paper develops a dual-domain optimization framework that combines the priors of (1) image- and (2) convolutional-coding-domains and offers generality to CS and other inverse imaging tasks. By converting this optimization framework into deep NN structures, we present a Dual-Domain Deep Convolutional Coding Network (D3C2-Net), which enjoys the ability to efficiently transmit high-capacity self-adaptive convolutional features across all its unfolded stages. Our theoretical analyses and experiments on simulated and real captured data, covering 2D and 3D natural, medical, and scientific signals, demonstrate the effectiveness, practicality, superior performance, and generalization ability of our method over other competing approaches and its significant potential in achieving a balance among accuracy, complexity, and interpretability. Code is available at https://github.com/lwq20020127/D3C2-Net.