UC Berkeley

This dissertation reports the development of radiation image reconstruction and uncertainty quantification algorithms incorporating Bayesian principles. The proposed algorithms effectively combat the ill-posed nature of radiation image reconstruction problems, while providing deeper insights into the physical quantities of interest through their uncertainty quantification capabilities. The first algorithm, dubbed Kullback-Leibler (KL) divergence maximum a posteriori expectation maximization (KLD MAP-EM), incorporates a sparsity-inducing prior distribution based on KL divergence. As a result, the algorithm yields parsimonious solution images effectively minimizing image artifacts caused by measurement noise, while accurately localizing radiation source hotspots. The algorithm is computationally efficient and requires minimal modification of the conventional maximum likelihood-expectation maximization (ML-EM) algorithm, making it readily applicable to a variety of radiation imaging applications where sparsity in solution images is required.

The second algorithm, named the Gaussian process prior (GPP) image reconstruction algorithm, imposes spatial correlations between image voxels through an underlying Gaussian process (GP) variable with a choice of link function. The algorithm is highly robust to overfitting, and the GP covariance kernel can be modified to incorporate structural priors, thereby enhancing the quality of reconstructed images. Furthermore, a complete Bayesian framework for uncertainty quantification and hyperparameter selection methods was developed for the GPP algorithm, leveraging the Laplace approximation and preconditioned Crank-Nikolson Markov Chain Monte Carlo (pCN MCMC). As a result, the GPP algorithm not only produces high quality reconstructed images but also provides accompanying uncertainty images, offering a more comprehensive understanding of the imaging subject. Furthermore, the method provides uncertainties for derived quantities such as radiation dose and total reconstructed activity, enhancing decision-making reliability in high-stakes scenarios. Lastly, the full-spectral GPP algorithm was developed, in which the following three different inverse problems are solved simultaneously: radiation spectra decomposition, deconvolution, and image reconstruction. The result is a novel algorithm decomposing a time-series of radiation energy spectra collected from a single, free-moving detector into their constituent contributions from radiological components, while reconstructing source distribution images corresponding to the identified components. The full-spectral GPP algorithm demonstrates exceptional performance, reconstructing source images and components even from low signal-to-noise ratio (SNR) measurements with fluctuating background contributions. Moreover, it enables deeper understanding of radiological environment by identifying salient radiological source and background features present in the imaging space.

The proposed algorithms have been rigorously tested using both simulated and real-world measurement data, that are challenging for conventional image reconstruction algorithms. Although primarily demonstrated for free-moving single detector imaging modality, these methods are broadly applicable across various imaging modalities, offering numerous avenues for future research.