# Deep Regularized Compound Gaussian Network for Solving Linear Inverse Problems

arXiv: https://arxiv.org/abs/2311.17248 · HTML: https://mlsanity.com/paper/2311.17248/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 58 references that are in the map.
- First posted on arXiv 28 Nov 2023.

## Builds on (most cited first, 14 of 14)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Deep Convolutional Neural Network for Inverse Problems in Imaging](https://mlsanity.com/paper/1611.03679/) (2016)
- [Algorithm Unrolling: Interpretable, Efficient Deep Learning for Signal and Image Processing](https://mlsanity.com/paper/1912.10557/) (2019)
- [Learned Primal-dual Reconstruction](https://mlsanity.com/paper/1707.06474/) (2017)
- [Coordinate Descent Algorithms](https://mlsanity.com/paper/1502.04759/) (2015)
- [Learning Proximal Operators: Using Denoising Networks for Regularizing Inverse Imaging Problems](https://mlsanity.com/paper/1704.03488/) (2017)
- [FISTA-Net: Learning A Fast Iterative Shrinkage Thresholding Network for Inverse Problems in Imaging](https://mlsanity.com/paper/2008.02683/) (2020)
- [Deep Gaussian Scale Mixture Prior for Spectral Compressive Imaging](https://mlsanity.com/paper/2103.07152/) (2021)
- [Memory-Augmented Deep Unfolding Network for Compressive Sensing](https://mlsanity.com/paper/2110.09766/) (2021)
- [Radon Inversion via Deep Learning](https://mlsanity.com/paper/1808.03015/) (2018)
- [Revisiting Normalized Gradient Descent: Fast Evasion of Saddle Points](https://mlsanity.com/paper/1711.05224/) (2017)
- [LEARN++: Recurrent Dual-Domain Reconstruction Network for Compressed Sensing CT](https://mlsanity.com/paper/2012.06983/) (2020)
- [Fast Stochastic Hierarchical Bayesian MAP for Tomographic Imaging](https://mlsanity.com/paper/1707.02336/) (2017)
- [A Compound Gaussian Least Squares Algorithm and Unrolled Network for Linear Inverse Problems](https://mlsanity.com/paper/2305.11120/) (2023)

## Built on by (most cited first, 1 of 1)

- [On Generalization Bounds for Deep Compound Gaussian Neural Networks](https://mlsanity.com/paper/2402.13106/) (2024)

## Abstract (arXiv)

Incorporating prior information into inverse problems, e.g. via maximum-a-posteriori estimation, is an important technique for facilitating robust inverse problem solutions. In this paper, we devise two novel approaches for linear inverse problems that permit problem-specific statistical prior selections within the compound Gaussian (CG) class of distributions. The CG class subsumes many commonly used priors in signal and image reconstruction methods including those of sparsity-based approaches. The first method developed is an iterative algorithm, called generalized compound Gaussian least squares (G-CG-LS), that minimizes a regularized least squares objective function where the regularization enforces a CG prior. G-CG-LS is then unrolled, or unfolded, to furnish our second method, which is a novel deep regularized (DR) neural network, called DR-CG-Net, that learns the prior information. A detailed computational theory on convergence properties of G-CG-LS and thorough numerical experiments for DR-CG-Net are provided. Due to the comprehensive nature of the CG prior, these experiments show that DR-CG-Net outperforms competitive prior art methods in tomographic imaging and compressive sensing, especially in challenging low-training scenarios.