# Accurate 2D Reconstruction for PET Scanners based on the Analytical White Image Model

arXiv: https://arxiv.org/abs/2306.17652 · HTML: https://mlsanity.com/paper/2306.17652/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 55 references that are in the map.
- First posted on arXiv 30 Jun 2023.

## Builds on (most cited first, 6 of 6)

- [Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoising](https://mlsanity.com/paper/1608.03981/) (2016)
- [Medical Image Synthesis with Context-Aware Generative Adversarial Networks](https://mlsanity.com/paper/1612.05362/) (2016)
- [Deep MR to CT Synthesis using Unpaired Data](https://mlsanity.com/paper/1708.01155/) (2017)
- [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)
- [Sampling and Reconstruction of Sparse Signals in Shift-Invariant Spaces: Generalized Shannon's Theorem Meets Compressive Sensing](https://mlsanity.com/paper/2010.15618/) (2020)

## Abstract (arXiv)

In this paper, we provide a precise mathematical model of crystal-to-crystal response which is used to generate the white image - a necessary compensation model needed to overcome the physical limitations of the PET scanner. We present a closed-form solution, as well as several accurate approximations, due to the complexity of the exact mathematical expressions. We prove, experimentally and analytically, that the difference between the best approximations and real crystal-to-crystal response is insignificant. The obtained responses are used to generate the white image compensation model. It can be written as a single closed-form expression making it easy to implement in known reconstruction methods. The maximum likelihood expectation maximization (MLEM) algorithm is modified and our white image model is integrated into it. The modified MLEM algorithm is not based on the system matrix, rather it is based on ray-driven projections and back-projections. The compensation model provides all necessary information about the system. Finally, we check our approach on synthetic and real data. For the real-world acquisition, we use the Raytest ClearPET camera for small animals and the NEMA NU 4-2008 phantom. The proposed approach overperforms competitive, non-compensated reconstruction methods.