Gamma-Ray Point-Source Localization and Sparse Image Reconstruction Using Poisson Likelihood

Gamma-ray imaging attempts to reconstruct the spatial and intensity distribution of gamma-emitting radionuclides from a set of measurements. Generally, this problem is solved by discretizing the spatial dimensions and employing the maximum likelihood expectation maximization (ML-EM) algorithm, with or without some form of regularization. While the generality of this formulation enables use in a wide variety of scenarios, it is susceptible to overfitting, limited by the discretization of spatial coordinates, and can be computationally expensive. We present a novel approach to 3D gamma-ray image reconstruction for scenarios where sparsity may be assumed, for example, radiological source search. In this paper, we first formulate a point-source localization (PSL) approach as an optimization problem, where both position and source intensity are continuous variables. We then extend and generalize this formulation to an iterative algorithm, called additive PSL (APSL), for sparse parametric image reconstruction. A set of simulated source search scenarios using a single non-directional detector are considered, finding improved image accuracy and computational efficiency with APSL over traditional grid-based approaches.