Recovery of missing data in partial geometry PET scanners: Compensation in projection space vs image space

Purpose Robust and reliable reconstruction of images from noisy and incomplete projection data holds significant potential for proliferation of cost‐effective medical imaging technologies. Since conventional reconstruction techniques can generate severe artifacts in the recovered images, a notable line of research constitutes development of appropriate algorithms to compensate for missing data and to reduce noise. In the present work, we investigate the effectiveness of state‐of‐the‐art methodologies developed for image inpainting and noise reduction to preserve the quality of reconstructed images from undersampled PET data. We aimed to assess and ascertain whether missing data recovery is best performed in the projection space prior to reconstruction or adjoined with the reconstruction step in image space. Methods Different strategies for data recovery were investigated using realistic patient derived phantoms (brain and abdomen) in PET scanners with partial geometry (small and large gap structures). Specifically, gap filling strategies in projection space were compared with reconstruction based compensation in image space. The methods used for filling the gap structure in sinogram PET data include partial differential equation based techniques (PDE), total variation (TV) regularization, discrete cosine transform(DCT)‐based penalized regression, and dictionary learning based inpainting (DLI). For compensation in image space, compressed sensing based image reconstruction methods were applied. These include the preconditioned alternating projection (PAPA) algorithm with first and higher order total variation (HOTV) regularization as well as dictionary learning based compressed sensing (DLCS). We additionally investigated the performance of the methods for recovery of missing data in the presence of simulated lesion. The impact of different noise levels in the undersampled sinograms on performance of the approaches were also evaluated. Results In our first study (brain imaging), DLI was shown to outperform other methods for small gap structure in terms of root mean square error (RMSE) and structural similarity (SSIM), though having relatively high computational cost. For large gap structure, HOTV‐PAPA produces better results. In the second study (abdomen imaging), again the best performance belonged to DLI for small gap, and HOTV‐PAPA for large gap. In our experiments for lesion simulation on patient brain phantom data, the best performance in term of contra