# Bayesian imaging inverse problem with SA-Roundtrip prior via HMC-pCN sampler

arXiv: https://arxiv.org/abs/2310.17817 · HTML: https://mlsanity.com/paper/2310.17817/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 46 references that are in the map.
- First posted on arXiv 24 Oct 2023.

## Builds on (most cited first, 20 of 20)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Large Scale GAN Training for High Fidelity Natural Image Synthesis](https://mlsanity.com/paper/1809.11096/) (2018)
- [Improved Training of Wasserstein GANs](https://mlsanity.com/paper/1704.00028/) (2017)
- [Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networks](https://mlsanity.com/paper/1511.06434/) (2015)
- [Spectral Normalization for Generative Adversarial Networks](https://mlsanity.com/paper/1802.05957/) (2018)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [Least Squares Generative Adversarial Networks](https://mlsanity.com/paper/1611.04076/) (2016)
- [Compressed Sensing using Generative Models](https://mlsanity.com/paper/1703.03208/) (2017)
- [Adversarial Regularizers in Inverse Problems](https://mlsanity.com/paper/1805.11572/) (2018)
- [Deep Bayesian Inversion](https://mlsanity.com/paper/1811.05910/) (2018)
- [Computed Tomography Reconstruction Using Deep Image Prior and Learned Reconstruction Methods](https://mlsanity.com/paper/2003.04989/) (2020)
- [Filter Response Normalization Layer: Eliminating Batch Dependence in the Training of Deep Neural Networks](https://mlsanity.com/paper/1911.09737/) (2019)
- [Solving Inverse Problems with a Flow-based Noise Model](https://mlsanity.com/paper/2003.08089/) (2020)
- [Solution of Physics-based Bayesian Inverse Problems with Deep Generative Priors](https://mlsanity.com/paper/2107.02926/) (2021)
- [Solving Inverse Problems by Joint Posterior Maximization with Autoencoding Prior](https://mlsanity.com/paper/2103.01648/) (2021)
- [Self-Score: Self-Supervised Learning on Score-Based Models for MRI Reconstruction](https://mlsanity.com/paper/2209.00835/) (2022)
- [Inference with Deep Generative Priors in High Dimensions](https://mlsanity.com/paper/1911.03409/) (2019)
- [DEVDAN: Deep Evolving Denoising Autoencoder](https://mlsanity.com/paper/1910.04062/) (2019)
- [Maximum-a-posteriori estimation with Bayesian confidence regions](https://mlsanity.com/paper/1602.08590/) (2016)
- [MCDIP-ADMM: Overcoming Overfitting in DIP-based CT reconstruction](https://mlsanity.com/paper/2304.03895/) (2023)

## Abstract (arXiv)

Bayesian inference with deep generative prior has received considerable interest for solving imaging inverse problems in many scientific and engineering fields. The selection of the prior distribution is learned from, and therefore an important representation learning of, available prior measurements. The SA-Roundtrip, a novel deep generative prior, is introduced to enable controlled sampling generation and identify the data's intrinsic dimension. This prior incorporates a self-attention structure within a bidirectional generative adversarial network. Subsequently, Bayesian inference is applied to the posterior distribution in the low-dimensional latent space using the Hamiltonian Monte Carlo with preconditioned Crank-Nicolson (HMC-pCN) algorithm, which is proven to be ergodic under specific conditions. Experiments conducted on computed tomography (CT) reconstruction with the MNIST and TomoPhantom datasets reveal that the proposed method outperforms state-of-the-art comparisons, consistently yielding a robust and superior point estimator along with precise uncertainty quantification.