Abstract
Deep learning-based methods have shown their superior performance for medical imaging, but their clinical application is still rare. One reason may come from their uncertainty. As data-driven models, deep learning-based methods are sensitive to imperfect data. Thus, it is important to quantify the uncertainty, especially for positron emission tomography (PET) denoising tasks where the noise is very similar to small tumors. In this paper, we proposed a Nouveau variational autoencoder (NVAE) based model using quantile regression loss for simultaneous PET image denoising and uncertainty estimation. Quantile regression loss was performed as the reconstruction loss to avoid the variance shrinkage problem caused by the traditional reconstruction probability loss. The variance and mean can be directly calculated from the estimated quantiles under the Logistic assumption, which is more efficient than Monte Carlo sampling. Experiment based on real \(^{11}\)C-DASB datasets verified that the denoised PET images of the proposed method have a higher mean(±SD) peak signal-to-noise ratio (PSNR) (40.64 ± 5.71) and structural similarity index measure (SSIM) (0.9807 ± 0.0063) than Unet-based denoising (PSNR, 36.18 ± 5.55; SSIM, 0.9614 ± 0.0121) and NVAE model using Monte Carlo sampling (PSNR, 37.00 ± 5.35; SSIM, 0.9671 ± 0.0095) methods.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Akrami, H., Joshi, A.A., Aydore, S., Leahy, R.M.: Addressing variance shrinkage in variational autoencoders using quantile regression. arXiv preprint arXiv:2010.09042 (2020)
Ballestar, L.M., Vilaplana, V.: MRI brain tumor segmentation and uncertainty estimation using 3D-UNet architectures. In: Crimi, A., Bakas, S. (eds.) BrainLes 2020. LNCS, vol. 12658, pp. 376–390. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-72084-1_34
Bishop, C.M.: Mixture density networks (1994)
Cui, J., Gong, K., Guo, N., Kim, K., Liu, H., Li, Q.: Unsupervised pet logan parametric image estimation using conditional deep image prior. Med. Image Anal. 80, 102519 (2022)
Cui, J., et al.: Populational and individual information based pet image denoising using conditional unsupervised learning. Phys. Med. Biol. 66(15), 155001 (2021)
Cui, J., et al.: Pet image denoising using unsupervised deep learning. Eur. J. Nucl. Med. Mol. Imaging 46(13), 2780–2789 (2019)
Cui, J., Gong, K., Han, P., Liu, H., Li, Q.: Unsupervised arterial spin labeling image superresolution via multiscale generative adversarial network. Med. Phys. 49(4), 2373–2385 (2022)
Cui, J., et al.: Pet denoising and uncertainty estimation based on NVAE model. In: 2021 IEEE Nuclear Science Symposium and Medical Imaging Conference Proceedings (NSS/MIC). IEEE (2021)
Fessler, J.A.: Approximate variance images for penalized-likelihood image reconstruction. In: 1997 IEEE Nuclear Science Symposium Conference Record, vol. 2, pp. 949–952. IEEE (1997)
Gal, Y., Ghahramani, Z.: Dropout as a Bayesian approximation: representing model uncertainty in deep learning. In: International Conference on Machine Learning, pp. 1050–1059. PMLR (2016)
Hao, J., et al.: Uncertainty-guided graph attention network for parapneumonic effusion diagnosis. Med. Image Anal. 75, 102217 (2022)
Hu, J., Shen, L., Sun, G.: Squeeze-and-excitation networks. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 7132–7141 (2018)
Huang, X., Shi, L., Suykens, J.A.: Support vector machine classifier with pinball loss. IEEE Trans. Pattern Anal. Mach. Intell. 36(5), 984–997 (2013)
Kingma, D.P., Welling, M.: Auto-encoding variational Bayes. arXiv preprint arXiv:1312.6114 (2013)
Kingma, D.P., Salimans, T., Jozefowicz, R., Chen, X., Sutskever, I., Welling, M.: Improved variational inference with inverse autoregressive flow. In: Advances in Neural Information Processing Systems, vol. 29 (2016)
Koenker, R., Bassett Jr, G.: Regression quantiles. Econometrica: J. Econometr. Soc. 33–50 (1978)
Lakshminarayanan, B., Pritzel, A., Blundell, C.: Simple and scalable predictive uncertainty estimation using deep ensembles. In: Advances in Neural Information Processing Systems, 30 (2017)
Laves, M.H., Ihler, S., Fast, J.F., Kahrs, L.A., Ortmaier, T.: Well-calibrated regression uncertainty in medical imaging with deep learning. In: Medical Imaging with Deep Learning, pp. 393–412. PMLR (2020)
MacKay, D.J.: A practical Bayesian framework for backpropagation networks. Neural Comput. 4(3), 448–472 (1992)
Nix, D.A., Weigend, A.S.: Estimating the mean and variance of the target probability distribution. In: Proceedings of 1994 IEEE International Conference on Neural Networks (ICNN 1994), vol. 1, pp. 55–60. IEEE (1994)
Qi, J., Leahy, R.M.: A theoretical study of the contrast recovery and variance of map reconstructions from pet data. IEEE Trans. Med. Imaging 18(4), 293–305 (1999)
Ramachandran, P., Zoph, B., Le, Q.V.: Searching for activation functions. arXiv preprint arXiv:1710.05941 (2017)
Salimans, T., Karpathy, A., Chen, X., Kingma, D.P.: Pixelcnn++: improving the pixelcnn with discretized logistic mixture likelihood and other modifications. arXiv preprint arXiv:1701.05517 (2017)
Sambyal, A.S., Krishnan, N.C., Bathula, D.R.: Towards reducing aleatoric uncertainty for medical imaging tasks. In: 2022 IEEE 19th International Symposium on Biomedical Imaging (ISBI), pp. 1–4. IEEE (2022)
Sohn, K., Lee, H., Yan, X.: Learning structured output representation using deep conditional generative models. Advances in Neural Information Processing Systems, vol. 28 (2015)
Sudarshan, V.P., Upadhyay, U., Egan, G.F., Chen, Z., Awate, S.P.: Towards lower-dose pet using physics-based uncertainty-aware multimodal learning with robustness to out-of-distribution data. Med. Image Anal. 73, 102187 (2021)
Thiagarajan, P., Khairnar, P., Ghosh, S.: Explanation and use of uncertainty obtained by Bayesian neural network classifiers for breast histopathology images. IEEE Trans. Med. Imaging 41, 815–825 (2021)
Vahdat, A., Kautz, J.: NVAE: a deep hierarchical variational autoencoder. arXiv preprint arXiv:2007.03898 (2020)
Wang, Z., Bovik, A.C., Sheikh, H.R., Simoncelli, E.P.: Image quality assessment: from error visibility to structural similarity. IEEE Trans. Image Process. 13(4), 600–612 (2004)
Yoshida, Y., Miyato, T.: Spectral norm regularization for improving the generalizability of deep learning. arXiv preprint arXiv:1705.10941 (2017)
Acknowledgements
This work was supported in part by the National Key Technology Research and Development Program of China (2020AAA0109502), the National Natural Science Foundation of China (U1809204, 62101488), the Key Research and Development Program of Zhejiang Province (2021C03029), the Talent Program of Zhejiang Province (2021R51004) and by China Postdoctoral Science Foundation (2021M692830)
Author information
Authors and Affiliations
Corresponding authors
Editor information
Editors and Affiliations
1 Electronic supplementary material
Below is the link to the electronic supplementary material.
Rights and permissions
Copyright information
© 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Cui, J. et al. (2022). PET Denoising and Uncertainty Estimation Based on NVAE Model Using Quantile Regression Loss. In: Wang, L., Dou, Q., Fletcher, P.T., Speidel, S., Li, S. (eds) Medical Image Computing and Computer Assisted Intervention – MICCAI 2022. MICCAI 2022. Lecture Notes in Computer Science, vol 13434. Springer, Cham. https://doi.org/10.1007/978-3-031-16440-8_17
Download citation
DOI: https://doi.org/10.1007/978-3-031-16440-8_17
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-16439-2
Online ISBN: 978-3-031-16440-8
eBook Packages: Computer ScienceComputer Science (R0)