2D PET Image Reconstruction Using Robust L1 Estimation of the Gaussian Mixture Model

An image or volume of interest in positron emission tomography (PET) is reconstructed from gamma rays emitted from a radioactive tracer, which are then captured and used to estimate the tracer’s location. The image or volume of interest is reconstructed by estimating the pixel or voxel values on a grid determined by the scanner. Such an approach is usually associated with limited resolution of the reconstruction, high computational complexity due to slow convergence and noisy results. This paper presents a novel method of PET image reconstruction using the underlying assumption that the originals of interest can be modelled using Gaussian mixture models. Parameters are estimated from one-dimensional projections using an iterative algorithm resembling the expectation-maximization algorithm. This presents a complex computational problem which is resolved by a novel approach that utilizes ${L_{1}}$ minimization.