Image recovery in PET scanners with partial detector rings using compressive sensing

Most PET scanners consist of tightly packed discrete detector rings to improve scanner efficiency. Our aim in this paper was to investigate the possibility of reducing the number of detector elements per ring (introduce gaps) while maintaining image quality by employing compressed sensing (CS) techniques. A uniform Ge-68 phantom (20 cm diameter and length) was imaged on a D-RX PET/CT scanner twice; once with all detectors operational (gold standard) and once with 4 detector blocks at each of 0, 90, 180 and 270 degrees turned off (partially sampled, 11 % off). Image recovery of the partially observed data was performed by minimizing the Total Variation (TV) of the derivatives of adjacent pixels in the image domain, while imposing a linear constraint of equity the product of system matrix and recovered image to the partially observed data. This minimization was repeated iteratively for a total of 100 iterations. The resultant corrected Image was then multiplied by the system matrix and the resultant sinogram was compared to the measured sinogram. In addition, the mean and maximum activity concentration in a ROI placed centrally over the phantom was computed between the resultant CS image, fully observed image (no gap- gold standard), and the partially sampled (with detector gap) image. The results of the CS recovery showed that the mean and maximum activity concentration difference in the recovered image was -0.74% and 2.27% respectively when compared to the gold standard while those for the partially observed images were 4.25% and 20%. Compressed sensing using TV approaches seems to be capable of generating accurate quantification of activity concentration from a partially sampled data set.