# On hallucinations in tomographic image reconstruction

**Authors:** Sayantan Bhadra, Varun A. Kelkar, Frank J. Brooks, Mark A. Anastasio  
**arXiv:** [2012.00646](https://arxiv.org/abs/2012.00646)  
**Date:** 2020-12-01  
**Summary page:** https://www.summarizepaper.com/en/paper/2012.00646v1/

## Key points

- Tomographic image reconstruction is a challenging problem in medical imaging
- It involves solving an ill-posed linear inverse problem
- Prior knowledge about the object being imaged is typically incorporated into the reconstruction process
- Deep neural networks have emerged as a promising approach for regularizing image reconstruction
- There is a need to understand the learned prior information and its ability to generalize to data outside the training distribution
- The authors propose a method to illustrate the effect of the prior imposed by a reconstruction method
- They decompose the image estimate into generalized measurement and null components
- They introduce the concept of a "hallucination map" to better understand the impact of the prior in regularized reconstruction methods
- Numerical studies using a stylized tomographic imaging modality are performed to analyze different reconstruction methods under their proposed formalism
- The authors discuss how different methods behave and provide insights into their effectiveness in mitigating hallucinations caused by inaccurate priors
- Accurate priors are important in avoiding false structures in medical imaging applications

## Summary

Tomographic image reconstruction is a challenging problem in medical imaging that involves solving an ill-posed linear inverse problem. To address this issue, prior knowledge about the object being imaged is typically incorporated into the reconstruction process. Recently, deep neural networks have emerged as a promising approach for regularizing image reconstruction by learning a prior from training images. However, there is still a need to understand the learned prior information and its ability to generalize to data that may lie outside the training distribution. In this study, conducted by Sayantan Bhadra, Varun A. Kelkar, Frank J. Brooks, and Mark A. Anastasio, the authors propose a method to illustrate the effect of the prior imposed by a reconstruction method. They decompose the image estimate into generalized measurement and null components and introduce the concept of a "hallucination map" to better understand the impact of the prior in regularized reconstruction methods. The authors perform numerical studies using a stylized tomographic imaging modality to analyze different reconstruction methods under their proposed formalism. By examining these numerical studies, they discuss how different methods behave and provide insights into their effectiveness in mitigating hallucinations caused by inaccurate priors. Overall, this work contributes to our understanding of deep neural networks' ability to learn priors for image reconstruction and highlights the importance of accurate priors in avoiding false structures in medical imaging applications. The findings from this study can potentially inform future developments in tomographic image reconstruction techniques and improve their reliability and accuracy.