Collaborative Computational Project in Synergistic Reconstruction for Biomedical Imaging

Synergistic Symposium 2019 Bayesian Methods

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Bangti Jin Uncertainty quantification for Poisson data

Poisson data arises in medical imaging modalities involving count data, e.g., SPECT and PET. Traditional reconstruction techniques are based on penalized likelihood estimates or more recently data driven approaches based on neural networks. However, these approaches can only give point estimates, and do not provide uncertainty information. This is largely due to high computational cost. In this talk, I will present our recent works on developing scalable techniques for uncertainty quantification with Poisson data, inspired by the developments in machine learning, e.g., variational inference, expectation propagation and deep neural networks.
A Sitek Quantitative PET using multi modality imaging and origin ensemble posterior

Quantitative positron emission tomography (PET) is of paramount importance in applications in neurology, oncology, and cardiology. Quantities such as standardized uptake values (SUVs) or ratio of SUVs (SUVRs) of different regions in images are frequently calculated and used clinically. Quantitative accuracy of PET and time-of-flight PET (TOF-PET) is hindered by many factors such as noisy data or finite resolution. Advanced state-of-the-art iterative reconstruction methods can be used to provide quantitative reconstructions, however estimations of uncertainty (covariance) is difficult especially for SUVRs where off-diagonal elements of covariance matrix need to be derived from complex data frequently provided in the list-mode format. Multimodality imaging (PET/CT, PET/MR) high-resolution structural information from CT and MR can be used to improve quantitation and, in longitudinal studies, consistency of region-of-interest (ROI) definition. We present statistics based approach to derive posterior distributions of SUVs and SUVRs. The approach is an alternative to iterative methods and provides estimations of SUVs and SUVRs and their Bayesian uncertainty. The method is based on origin ensemble (OE) concept and uses high resolution modality data for identification of ROIs. The approach is well suited for reconstructions list-mode and binned PET TOF-PET CT/MR data with corrections for physical factors affecting quantitation (finite resolution, scatter, positron range, multiple coincidences, etc.). Introduction to the theory of OE is provided and examples of applications of the methods discussed.
M F Pierucci PET reconstruction of the posterior image probability, including multimodal images

In PET image reconstruction, it would be useful to obtain the entire posterior probability distribution of the image, because it allows for both estimating image intensity and assessing the uncertainty of the estimation, thus leading to more reliable interpretation. We propose a new entirely probabilistic model: the prior is a distribution over possible smooth regions (distance-driven Chinese restaurant process), and the posterior distribution is estimated using a Gibbs MCMC sampler. Data from other modalities (here one or several MR images) are introduced into the model as additional observed data, providing side information about likely smooth regions in the image. The reconstructed image is the posterior mean, and the uncertainty is presented as an image of the size of 95% posterior intervals. The reconstruction was compared to MLEM and OSEM algorithms, with and without post-smoothing, and to a penalized ML or MAP method that also uses additional images from other modalities. Qualitative and quantitative tests were performed on realistic simulated data with statistical replicates and on several clini- cal examinations presenting pathologies. The proposed method presents appealing properties in terms of obtained bias, variance, spatial regularization, and use of multimodal data, and produces in addition potentially valuable uncertainty information.