Segmentation based WLS and ML attenuation correction methods for positron emission tomography

In this paper, we present weighted least-squares (WLS) and maximum likelihood (ML) algorithms for reconstructing transmission images from positron emission tomography (PET) transmission data. The key idea behind the algorithms is that the problem of minimizing the WLS and ML objective functions can be viewed as a sequence of least-squares minimization problems. This viewpoint follows from using certain quadratic functions that serve as surrogate functions for the WLS and ML objective functions. To illustrate the utility of the algorithms, we reconstruct transmission images from short-duration phantom data. The resulting images are then segmented using a hidden Markov model based segmentation algorithm. From the simulation results, it is evident that the algorithms converge fast and produce transmission images that can be segmented and improved using region dependent smoothing