# Rethinking the CSC Model for Natural Images

arXiv: https://arxiv.org/abs/1909.05742 · HTML: https://mlsanity.com/paper/1909.05742/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Sep 2019.

## Built on by (most cited first, 21 of 21)

- [Efficient Diffusion Model for Image Restoration by Residual Shifting](https://mlsanity.com/paper/2403.07319/) (2024)
- [A Trainable Spectral-Spatial Sparse Coding Model for Hyperspectral Image Restoration](https://mlsanity.com/paper/2111.09708/) (2021)
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- [Image Super-Resolution with Deep Dictionary](https://mlsanity.com/paper/2207.09228/) (2022)
- [Hybrid ISTA: Unfolding ISTA With Convergence Guarantees Using Free-Form Deep Neural Networks](https://mlsanity.com/paper/2204.11640/) (2022)
- [Panchromatic and Multispectral Image Fusion via Alternating Reverse Filtering Network](https://mlsanity.com/paper/2210.08181/) (2022)
- [On the convergence of group-sparse autoencoders](https://mlsanity.com/paper/2102.07003/) (2021)
- [CDLNet: Noise-Adaptive Convolutional Dictionary Learning Network for Blind Denoising and Demosaicing](https://mlsanity.com/paper/2112.00913/) (2021)
- [Poisson2Sparse: Self-Supervised Poisson Denoising From a Single Image](https://mlsanity.com/paper/2206.01856/) (2022)
- [Deep learning based dictionary learning and tomographic image reconstruction](https://mlsanity.com/paper/2108.11730/) (2021)
- [Gabor is Enough: Interpretable Deep Denoising with a Gabor Synthesis Dictionary Prior](https://mlsanity.com/paper/2204.11146/) (2022)
- [Pivotal Auto-Encoder via Self-Normalizing ReLU](https://mlsanity.com/paper/2406.16052/) (2024)
- [Controlled Learning of Pointwise Nonlinearities in Neural-Network-Like Architectures](https://mlsanity.com/paper/2408.13114/) (2024)
- [Universal Architectures for the Learning of Polyhedral Norms and Convex Regularizers](https://mlsanity.com/paper/2503.19190/) (2025)
- [CDLNet: Robust and Interpretable Denoising Through Deep Convolutional Dictionary Learning](https://mlsanity.com/paper/2103.04779/) (2021)
- [Improved Image Generation via Sparse Modeling](https://mlsanity.com/paper/2104.00464/) (2021)
- [Learned Interpretable Residual Extragradient ISTA for Sparse Coding](https://mlsanity.com/paper/2106.11970/) (2021)
- [Learning unfolded networks with a cyclic group structure](https://mlsanity.com/paper/2211.09238/) (2022)
- [Learning Linear Groups in Neural Networks](https://mlsanity.com/paper/2305.18552/) (2023)
- [A deep dictionary network-based foundation model for ultra-low-dose CT denoising](https://mlsanity.com/paper/2609.16031/) (2026)

## Abstract (arXiv)

Sparse representation with respect to an overcomplete dictionary is often used when regularizing inverse problems in signal and image processing. In recent years, the Convolutional Sparse Coding (CSC) model, in which the dictionary consists of shift-invariant filters, has gained renewed interest. While this model has been successfully used in some image processing problems, it still falls behind traditional patch-based methods on simple tasks such as denoising. In this work we provide new insights regarding the CSC model and its capability to represent natural images, and suggest a Bayesian connection between this model and its patch-based ancestor. Armed with these observations, we suggest a novel feed-forward network that follows an MMSE approximation process to the CSC model, using strided convolutions. The performance of this supervised architecture is shown to be on par with state of the art methods while using much fewer parameters.