The implementation of emission-computed tomography (ECT), including positron emission tomography and single-photon emission-computed tomography, has been an important research topic in recent years and is of significant and practical importance. However, the slow rate of convergence and the computational complexity have severely impeded the efficient implementation of iterative reconstruction. By combining the maximum-likelihood expectation maximization (MLEM) iteratively along with the Beltrami filter, this paper proposes a new approach to reformulate the MLEM algorithm. Beltrami filtering is applied to an image obtained using the MLEM algorithm for each iteration. The role of Beltrami filtering is to remove mainly out-of-focus slice blurs, which are artifacts present in most existing images. To improve the quality of an image reconstructed using MLEM, the Beltrami filter employs similar structures, which in turn reduce the number of errors in the reconstructed image. Numerical image reconstruction tomography experiments have demonstrated the performance capability of the proposed algorithm in terms of an increase in signal-to-noise ratio (SNR) and the recovery of fine details that can be hidden in the data. The SNR and visual inspections of the reconstructed images are significantly improved compared to those of a standard MLEM. We conclude that the proposed algorithm provides an edge-preserving image reconstruction and substantially suppress noise and edge artifacts.

Positron emission tomography (PET) is an imaging technique that generates 3D detail of physiological processes at the cellular level. The technique requires a radioactive tracer, which decays and releases a positron that collides with an electron; consequently, annihilation photons are emitted, which can be measured. The purpose of PET is to use the measurement of photons to reconstruct the distribution of radioisotopes in the body. Currently, PET is undergoing a revamp, with advancements in data measurement instruments and the computing methods used to create the images. These computer methods are required to solve the inverse problem of “image reconstruction from projection”. This paper proposes a novel kernel-based regularization technique for maximum-likelihood expectation-maximization ( $\kappa$ -MLEM) to reconstruct the image. Compared to standard MLEM, the proposed algorithm is more robust and is more effective in removing background noise, whilst preserving the edges; this suppresses image artifacts, such as out-of-focus slice blur.