A focus of attention EM algorithm for PET image reconstruction

Positron Emission Tomography (PET) image reconstruction can be done using the Expectation Maximization (EM) algorithm to optimize a likelihood function based on emissions. The EM algorithm utilizes a large probability matrix and thus can be computationally expensive. Consequently, reducing the size (number of nonzeros) of this matrix can make the algorithm significantly more efficient. We use a parallel implementation of the EM algorithm in which masking is used to reduce computation. A mask indicating relevant emissions is obtained through an algorithm to determine areas of background level emissions. Another mask indicating the relevant portion of the image space is then determined from the first mask and the scanner geometry. The reduced probability matrix used by the EM algorithm then represents the correlation between emissions and the relevant portion of the image space. The overhead required to eliminate nonzeros with masking is minimal. How-ever, a limited probability matrix can be constructed using fewer resources and can result in faster EM iterations. Considering all factors, this focus of attention technique can reduce required time and memory by approximately fifty percent without loss in the quality of reconstructed images.