Analysis of organ uniformity in low count density penalized likelihood PET images

We evaluated the organ uniformity properties of post-smoothed OSEM and penalized-likelihood (PL) images reconstructed with quadratic and non-quadratic penalties from low count PET datasets. Tumor contrast, background noise strength and background noise correlation length properties were jointly used to compare bias, variance and covariance tradeoffs within uniform organs in PL and post-smoothed OSEM images. Contrast was measured as the ratio of mean tumor and mean background activities. Noise variance was measured as the average ensemble standard deviation of the background voxels. Noise correlation lengths were measured indirectly via a non-uniformity metric as the standard deviation of the means inside 15 background spheres. Short noise correlation lengths gave small non-uniformity values while those comparable to sphere dimensions resulted in larger values. Simulated 2D and 3D datasets with less than 3 counts per sinogram bin were reconstructed using post-smoothed OSEM and PL with quadratic, logcosh, Huber and generalized Gaussian penalties. The generalized Gaussian penalty with proper parameter selection, was able to provide images with both higher contrast and shorter noise correlation lengths at matched noise strength. Other penalties resulted in images with shorter noise correlation lengths at approximately matched contrast and noise strengths. Overall, PL reconstructions resulted in fewer background regions to be confused with tumors compared to OSEM, without compromising contrast and noise strength properties.