Reconstruction of Positron Emission Tomography Images Using Gaussian Curvature

Positron emission tomography (PET) provides images of metabolic activity in the body, and it is used in the research, monitoring, and diagnosis of several diseases. However, the raw data produced by the scanner are severely corrupted by noise, causing a degraded quality in the reconstructed images. In this paper, we proposed a reconstruction algorithm to improve the image reconstruction process, addressing the problem from a variational geometric perspective. We proposed using the weighted Gaussian curvature (WGC) as a regularization term to better deal with noise and preserve the original geometry of the image, such as the lesion structure. In other contexts, the WGC term has been found to have excellent capabilities for preserving borders and structures of low gradient magnitude, such as ramp-like structures; at the same time, it effectively removes noise in the image. We presented several experiments aimed at evaluating contrast and lesion detectability in the reconstructed images. The results for simulated images and real data showed that our proposed algorithm effectively preserves lesions and removes noise.