# Learning Multiscale Convolutional Dictionaries for Image Reconstruction

arXiv: https://arxiv.org/abs/2011.12815 · HTML: https://mlsanity.com/paper/2011.12815/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Nov 2020.

## Built on by (most cited first, 11 of 11)

- [Conditional Injective Flows for Bayesian Imaging](https://mlsanity.com/paper/2204.07664/) (2022)
- [Sinogram upsampling using Primal-Dual UNet for undersampled CT and radial MRI reconstruction](https://mlsanity.com/paper/2112.13443/) (2021)
- [Deep Unfolding Convolutional Dictionary Model for Multi-Contrast MRI Super-resolution and Reconstruction](https://mlsanity.com/paper/2309.01171/) (2023)
- [Glimpse: Generalized Locality for Scalable and Robust CT](https://mlsanity.com/paper/2401.00816/) (2024)
- [FunkNN: Neural Interpolation for Functional Generation](https://mlsanity.com/paper/2212.14042/) (2022)
- [Deep Injective Prior for Inverse Scattering](https://mlsanity.com/paper/2301.03092/) (2023)
- [Learning of Patch-Based Smooth-Plus-Sparse Models for Image Reconstruction](https://mlsanity.com/paper/2412.13070/) (2024)
- [LoFi: Neural Local Fields for Scalable Image Reconstruction](https://mlsanity.com/paper/2411.04995/) (2024)
- [Enhanced Low-Dose CT Image Reconstruction by Domain and Task Shifting Gaussian Denoisers](https://mlsanity.com/paper/2403.03551/) (2024)
- [Enhanced artificial intelligence-based diagnosis using CBCT with internal denoising: Clinical validation for discrimination of fungal ball, sinusitis, and normal cases in the maxillary sinus](https://mlsanity.com/paper/2211.15950/) (2022)
- [Inversion of Magnetic Data using Learned Dictionaries and Scale Space](https://mlsanity.com/paper/2502.05451/) (2025)

## Abstract (arXiv)

Convolutional neural networks (CNNs) have been tremendously successful in solving imaging inverse problems. To understand their success, an effective strategy is to construct simpler and mathematically more tractable convolutional sparse coding (CSC) models that share essential ingredients with CNNs. Existing CSC methods, however, underperform leading CNNs in challenging inverse problems. We hypothesize that the performance gap may be attributed in part to how they process images at different spatial scales: While many CNNs use multiscale feature representations, existing CSC models mostly rely on single-scale dictionaries. To close the performance gap, we thus propose a multiscale convolutional dictionary structure. The proposed dictionary structure is derived from the U-Net, arguably the most versatile and widely used CNN for image-to-image learning problems. We show that incorporating the proposed multiscale dictionary in an otherwise standard CSC framework yields performance competitive with state-of-the-art CNNs across a range of challenging inverse problems including CT and MRI reconstruction. Our work thus demonstrates the effectiveness and scalability of the multiscale CSC approach in solving challenging inverse problems.