# Unsupervised PET Reconstruction from a Bayesian Perspective

arXiv: https://arxiv.org/abs/2110.15568 · HTML: https://mlsanity.com/paper/2110.15568/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 64 references that are in the map.
- First posted on arXiv 29 Oct 2021.

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

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Faster R-CNN: Towards Real-Time Object Detection with Region Proposal Networks](https://mlsanity.com/paper/1506.01497/) (2015)
- [Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoising](https://mlsanity.com/paper/1608.03981/) (2016)
- [Deep Image Prior](https://mlsanity.com/paper/1711.10925/) (2017)
- [Stochastic Gradient Hamiltonian Monte Carlo](https://mlsanity.com/paper/1402.4102/) (2014)
- [The Little Engine that Could: Regularization by Denoising (RED)](https://mlsanity.com/paper/1611.02862/) (2016)
- [Low-Dose CT with a Residual Encoder-Decoder Convolutional Neural Network (RED-CNN)](https://mlsanity.com/paper/1702.00288/) (2017)
- [Low Dose CT Image Denoising Using a Generative Adversarial Network with Wasserstein Distance and Perceptual Loss](https://mlsanity.com/paper/1708.00961/) (2017)
- [Preconditioned Stochastic Gradient Langevin Dynamics for Deep Neural Networks](https://mlsanity.com/paper/1512.07666/) (2015)
- [DeepRED: Deep Image Prior Powered by RED](https://mlsanity.com/paper/1903.10176/) (2019)
- [The promises and pitfalls of Stochastic Gradient Langevin Dynamics](https://mlsanity.com/paper/1811.10072/) (2018)
- [A Bayesian Perspective on the Deep Image Prior](https://mlsanity.com/paper/1904.07457/) (2019)
- [DeepPET: A deep encoder-decoder network for directly solving the PET reconstruction inverse problem](https://mlsanity.com/paper/1804.07851/) (2018)
- [Iterative PET Image Reconstruction Using Convolutional Neural Network Representation](https://mlsanity.com/paper/1710.03344/) (2017)
- [MAGIC: Manifold and Graph Integrative Convolutional Network for Low-Dose CT Reconstruction](https://mlsanity.com/paper/2008.00406/) (2020)
- [Boosting of Image Denoising Algorithms](https://mlsanity.com/paper/1502.06220/) (2015)
- [Deep BCD-Net Using Identical Encoding-Decoding CNN Structures for Iterative Image Recovery](https://mlsanity.com/paper/1802.07129/) (2018)
- [Factor analysis of dynamic PET images: beyond Gaussian noise](https://mlsanity.com/paper/1807.11455/) (2018)

## Abstract (arXiv)

Positron emission tomography (PET) reconstruction has become an ill-posed inverse problem due to low-count projection data, and a robust algorithm is urgently required to improve imaging quality. Recently, the deep image prior (DIP) has drawn much attention and has been successfully applied in several image restoration tasks, such as denoising and inpainting, since it does not need any labels (reference image). However, overfitting is a vital defect of this framework. Hence, many methods have been proposed to mitigate this problem, and DeepRED is a typical representation that combines DIP and regularization by denoising (RED). In this article, we leverage DeepRED from a Bayesian perspective to reconstruct PET images from a single corrupted sinogram without any supervised or auxiliary information. In contrast to the conventional denoisers customarily used in RED, a DnCNN-like denoiser, which can add an adaptive constraint to DIP and facilitate the computation of derivation, is employed. Moreover, to further enhance the regularization, Gaussian noise is injected into the gradient updates, deriving a Markov chain Monte Carlo (MCMC) sampler. Experimental studies on brain and whole-body datasets demonstrate that our proposed method can achieve better performance in terms of qualitative and quantitative results compared to several classic and state-of-the-art methods.