A weighted least squares PET image reconstruction method using iterative coordinate descent algorithms

In this paper, we present an image reconstruction method for positron emission tomography (PET) based on weighted least squares (WLS) objective function. Unlike a usual WLS algorithm, the proposed method, which we call it ICD-WLS, minimizes the WLS objective function using iterative coordinate descent (ICD) method in a sequence of small "hidden" data spaces. Although ICD-WLS uses a strategy to update parameter sequentially just like common ICD method, however, the use of these small "hidden" data spaces makes the ICD-WLS method converge more faster and produce reconstructed images with greater contrast and detail than the usual WLS methods. The OS algorithm is also used to accelerate image reconstruction for ICD-WLS. The experimental results show that the proposed method is more effective even if the projection data include statistic noise.