# Learning Sparse and Low-Rank Priors for Image Recovery via Iterative Reweighted Least Squares Minimization

arXiv: https://arxiv.org/abs/2304.10536 · HTML: https://mlsanity.com/paper/2304.10536/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 60 references that are in the map.
- First posted on arXiv 20 Apr 2023.

## Builds on (most cited first, 18 of 18)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Instance Normalization: The Missing Ingredient for Fast Stylization](https://mlsanity.com/paper/1607.08022/) (2016)
- [Deep Equilibrium Models](https://mlsanity.com/paper/1909.01377/) (2019)
- [Algorithm Unrolling: Interpretable, Efficient Deep Learning for Signal and Image Processing](https://mlsanity.com/paper/1912.10557/) (2019)
- [Learning Deep CNN Denoiser Prior for Image Restoration](https://mlsanity.com/paper/1704.03264/) (2017)
- [Toward Real-World Single Image Super-Resolution: A New Benchmark and A New Model](https://mlsanity.com/paper/1904.00523/) (2019)
- [The Little Engine that Could: Regularization by Denoising (RED)](https://mlsanity.com/paper/1611.02862/) (2016)
- [Deep Unfolding Network for Image Super-Resolution](https://mlsanity.com/paper/2003.10428/) (2020)
- [Blind Super-Resolution Kernel Estimation using an Internal-GAN](https://mlsanity.com/paper/1909.06581/) (2019)
- [Residual Feature Distillation Network for Lightweight Image Super-Resolution](https://mlsanity.com/paper/2009.11551/) (2020)
- [Sparse Modeling for Image and Vision Processing](https://mlsanity.com/paper/1411.3230/) (2014)
- [DWDN: Deep Wiener Deconvolution Network for Non-Blind Image Deblurring](https://mlsanity.com/paper/2103.09962/) (2021)
- [Weighted Schatten p-Norm Minimization for Image Denoising and Background Subtraction](https://mlsanity.com/paper/1512.01003/) (2015)
- [Iterative Joint Image Demosaicking and Denoising using a Residual Denoising Network](https://mlsanity.com/paper/1807.06403/) (2018)
- [Low Rank Regularization: A Review](https://mlsanity.com/paper/1808.04521/) (2018)
- [A Scalable Second Order Method for Ill-Conditioned Matrix Completion from Few Samples](https://mlsanity.com/paper/2106.02119/) (2021)

## Built on by (most cited first, 10 of 10)

- [Speckle2Self: Self-Supervised Ultrasound Speckle Reduction Without Clean Data](https://mlsanity.com/paper/2507.06828/) (2025)
- [DEALing with Image Reconstruction: Deep Attentive Least Squares](https://mlsanity.com/paper/2502.04079/) (2025)
- [Stability of Data-Dependent Ridge-Regularization for Inverse Problems](https://mlsanity.com/paper/2406.12289/) (2024)
- [Iteratively Refined Image Reconstruction with Learned Attentive Regularizers](https://mlsanity.com/paper/2407.06608/) (2024)
- [Recovering Simultaneously Structured Data via Non-Convex Iteratively Reweighted Least Squares](https://mlsanity.com/paper/2306.04961/) (2023)
- [Iterative Reweighted Least Squares Networks With Convergence Guarantees for Solving Inverse Imaging Problems](https://mlsanity.com/paper/2308.05745/) (2023)
- [Robust Two-View Geometry Estimation with Implicit Differentiation](https://mlsanity.com/paper/2410.17983/) (2024)
- [Prototype Clustered Diffusion Models for Versatile Inverse Problems](https://mlsanity.com/paper/2407.09768/) (2024)
- [Variational Bayesian Inference for Tensor Robust Principal Component Analysis](https://mlsanity.com/paper/2412.18717/) (2024)
- [Dynamic Proximal Gradient Algorithms for Schatten-p Quasi-Norm Regularized Problems](https://mlsanity.com/paper/2603.00333/) (2026)

## Abstract (arXiv)

We introduce a novel optimization algorithm for image recovery under learned sparse and low-rank constraints, which we parameterize as weighted extensions of the ℓpp-vector and mathcal Spp Schatten-matrix quasi-norms for 0!<p!≤1, respectively. Our proposed algorithm generalizes the Iteratively Reweighted Least Squares (IRLS) method, used for signal recovery under ℓ1 and nuclear-norm constrained minimization. Further, we interpret our overall minimization approach as a recurrent network that we then employ to deal with inverse low-level computer vision problems. Thanks to the convergence guarantees that our IRLS strategy offers, we are able to train the derived reconstruction networks using a memory-efficient implicit back-propagation scheme, which does not pose any restrictions on their effective depth. To assess our networks' performance, we compare them against other existing reconstruction methods on several inverse problems, namely image deblurring, super-resolution, demosaicking and sparse recovery. Our reconstruction results are shown to be very competitive and in many cases outperform those of existing unrolled networks, whose number of parameters is orders of magnitude higher than that of our learned models.