# Sparse Bayesian Generative Modeling for Compressive Sensing

arXiv: https://arxiv.org/abs/2411.09483 · HTML: https://mlsanity.com/paper/2411.09483/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 50 references that are in the map.
- First posted on arXiv 14 Nov 2024.

## Builds on (most cited first, 21 of 21)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Deep Image Prior](https://mlsanity.com/paper/1711.10925/) (2017)
- [An Introduction to Variational Autoencoders](https://mlsanity.com/paper/1906.02691/) (2019)
- [The Perception-Distortion Tradeoff](https://mlsanity.com/paper/1711.06077/) (2017)
- [Predictive Uncertainty Estimation via Prior Networks](https://mlsanity.com/paper/1802.10501/) (2018)
- [Deep Evidential Regression](https://mlsanity.com/paper/1910.02600/) (2019)
- [Compressed Sensing using Generative Models](https://mlsanity.com/paper/1703.03208/) (2017)
- [Deep Decoder: Concise Image Representations from Untrained Non-convolutional Networks](https://mlsanity.com/paper/1810.03982/) (2018)
- [Prior and Posterior Networks: A Survey on Evidential Deep Learning Methods For Uncertainty Estimation](https://mlsanity.com/paper/2110.03051/) (2021)
- [Robust Compressed Sensing using Generative Models](https://mlsanity.com/paper/2006.09461/) (2020)
- [Task-Aware Compressed Sensing with Generative Adversarial Networks](https://mlsanity.com/paper/1802.01284/) (2018)
- [An Asymptotically MSE-Optimal Estimator based on Gaussian Mixture Models](https://mlsanity.com/paper/2112.12499/) (2021)
- [Cryo-CARE: Content-Aware Image Restoration for Cryo-Transmission Electron Microscopy Data](https://mlsanity.com/paper/1810.05420/) (2018)
- [On the Asymptotic Mean Square Error Optimality of Diffusion Models](https://mlsanity.com/paper/2403.02957/) (2024)
- [Leveraging Variational Autoencoders for Parameterized MMSE Estimation](https://mlsanity.com/paper/2307.05352/) (2023)
- [RandNet: deep learning with compressed measurements of images](https://mlsanity.com/paper/1908.09258/) (2019)
- [Towards Deep Learning-aided Wireless Channel Estimation and Channel State Information Feedback for 6G](https://mlsanity.com/paper/2209.01724/) (2022)
- [HKF: Hierarchical Kalman Filtering with Online Learned Evolution Priors for Adaptive ECG Denoising](https://mlsanity.com/paper/2210.12807/) (2022)
- [Efficient Dictionary Learning via Very Sparse Random Projections](https://mlsanity.com/paper/1504.01169/) (2015)

## Abstract (arXiv)

This work addresses the fundamental linear inverse problem in compressive sensing (CS) by introducing a new type of regularizing generative prior. Our proposed method utilizes ideas from classical dictionary-based CS and, in particular, sparse Bayesian learning (SBL), to integrate a strong regularization towards sparse solutions. At the same time, by leveraging the notion of conditional Gaussianity, it also incorporates the adaptability from generative models to training data. However, unlike most state-of-the-art generative models, it is able to learn from a few compressed and noisy data samples and requires no optimization algorithm for solving the inverse problem. Additionally, similar to Dirichlet prior networks, our model parameterizes a conjugate prior enabling its application for uncertainty quantification. We support our approach theoretically through the concept of variational inference and validate it empirically using different types of compressible signals.