# Learned Convolutional Sparse Coding

arXiv: https://arxiv.org/abs/1711.00328 · HTML: https://mlsanity.com/paper/1711.00328/

## Key facts

- Cited by 26 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Nov 2017.

## Built on by (most cited first, 26 of 26)

- [Learning to Optimize: A Primer and A Benchmark](https://mlsanity.com/paper/2103.12828/) (2021)
- [LRRNet: A Novel Representation Learning Guided Fusion Network for Infrared and Visible Images](https://mlsanity.com/paper/2304.05172/) (2023)
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- [Revisiting Sparse Convolutional Model for Visual Recognition](https://mlsanity.com/paper/2210.12945/) (2022)
- [All-weather Multi-Modality Image Fusion: Unified Framework and 100k Benchmark](https://mlsanity.com/paper/2402.02090/) (2024)
- [Generalization Error Bounds for Iterative Recovery Algorithms Unfolded as Neural Networks](https://mlsanity.com/paper/2112.04364/) (2021)
- [Mixed X-Ray Image Separation for Artworks with Concealed Designs](https://mlsanity.com/paper/2201.09167/) (2022)
- [Hybrid ISTA: Unfolding ISTA With Convergence Guarantees Using Free-Form Deep Neural Networks](https://mlsanity.com/paper/2204.11640/) (2022)
- [D3C2-Net: Dual-Domain Deep Convolutional Coding Network for Compressive Sensing](https://mlsanity.com/paper/2207.13560/) (2022)
- [Closed-Loop Transcription via Convolutional Sparse Coding](https://mlsanity.com/paper/2302.09347/) (2023)
- [Fast Window-Based Event Denoising with Spatiotemporal Correlation Enhancement](https://mlsanity.com/paper/2402.09270/) (2024)
- [CDLNet: Noise-Adaptive Convolutional Dictionary Learning Network for Blind Denoising and Demosaicing](https://mlsanity.com/paper/2112.00913/) (2021)
- [SINET: Sparsity-driven Interpretable Neural Network for Underwater Image Enhancement](https://mlsanity.com/paper/2409.01022/) (2024)
- [l0-Regularized Sparse Coding-based Interpretable Network for Multi-Modal Image Fusion](https://mlsanity.com/paper/2411.04519/) (2024)
- [DuRIN: A Deep-unfolded Sparse Seismic Reflectivity Inversion Network](https://mlsanity.com/paper/2104.04704/) (2021)
- [Gabor is Enough: Interpretable Deep Denoising with a Gabor Synthesis Dictionary Prior](https://mlsanity.com/paper/2204.11146/) (2022)
- [MambaReg: Mamba-Based Disentangled Convolutional Sparse Coding for Unsupervised Deformable Multi-Modal Image Registration](https://mlsanity.com/paper/2411.01399/) (2024)
- [CDLNet: Robust and Interpretable Denoising Through Deep Convolutional Dictionary Learning](https://mlsanity.com/paper/2103.04779/) (2021)
- [NuSPAN: A Proximal Average Network for Nonuniform Sparse Model -- Application to Seismic Reflectivity Inversion](https://mlsanity.com/paper/2105.00003/) (2021)
- [Learned Interpretable Residual Extragradient ISTA for Sparse Coding](https://mlsanity.com/paper/2106.11970/) (2021)
- [A statistical perspective on algorithm unrolling models for inverse problems](https://mlsanity.com/paper/2311.06395/) (2023)
- [On The Relationship Between Universal Adversarial Attacks And Sparse Representations](https://mlsanity.com/paper/2311.08265/) (2023)
- [Cross-Sequence Semi-Supervised Learning for Multi-Parametric MRI-Based Visual Pathway Delineation](https://mlsanity.com/paper/2505.19733/) (2025)
- [Hyperspectral Unmixing with 3D Convolutional Sparse Coding and Projected Simplex Volume Maximization](https://mlsanity.com/paper/2512.05674/) (2025)
- [Mitigating Content Shift and Hallucination in GenAI Image Editing via Structural Refinement](https://mlsanity.com/paper/2605.30437/) (2026)
- [MODAL: Multi-Modal Object Re-ID via Model-Driven Sparse Decoupling and Text-Image Differential Filtering](https://mlsanity.com/paper/2608.15096/) (2026)

## Abstract (arXiv)

We propose a convolutional recurrent sparse auto-encoder model. The model consists of a sparse encoder, which is a convolutional extension of the learned ISTA (LISTA) method, and a linear convolutional decoder. Our strategy offers a simple method for learning a task-driven sparse convolutional dictionary (CD), and producing an approximate convolutional sparse code (CSC) over the learned dictionary. We trained the model to minimize reconstruction loss via gradient decent with back-propagation and have achieved competitive results to KSVD image denoising and to leading CSC methods in image inpainting requiring only a small fraction of their run-time.