Fast algebraic reconstruction using subsets of PET data

Filtered backprojection (FBP) method for positron emission tomography (PET) produces artifacts in the reconstructed images when the measurement system has the shift-variant characteristics. On the other hand, the conventional algebraic reconstruction methods, such as the generalized analytic reconstruction from discrete samples (CARDS), the natural pixel decomposition (NPD) and the algebraic reconstruction technique (ART), can correct these characteristics, while these methods have computational burden. Here, the authors propose a fast image reconstruction method for PET using an algebraic technique. In this method, a reconstruction operator is given approximately using subsets of sensitivity functions. The subsets are designed by selecting the sensitivity functions that have high sensitivity to each point to be reconstructed and by keeping an accuracy of the reconstructed images. The proposed method was applied to simulated data for the scanner, ECAT EXACT HR+ (Siemens/CTI) working in the 2D mode. This result shows that the proposed method produces images with almost the same quality as the conventional algebraic methods do and has a similar computation time to FBP method.