A PDE based expectation maximization algorithm adapted to Poisson noise for medical image reconstruction

Computerized Tomography and Positron Emission Tomography (CT/PET) is an effective and indispensable imaging tool for the application of medical image reconstruction. The noise contained in the data measured by imaging instruments is primarily Poisson type and decreasing the noise has the potential to optimize the quality of CT/PET images. But the traditional iterative reconstruction algorithms of CT/PET cannot effectively filter the noise. Recently anisotropic diffusion (AD) based nonlinear filter is introduced into tomography reconstruction that purports to filter the noise without blurring edges. This paper introduces and evaluates a hybrid approach to regularized maximum likelihood expectation maximization (MLEM) iterative reconstruction technique with Poisson variability. Regularization is achieved by penalizing MLEM with Anisotropic diffusion (AD) filter to form hybrid method for CT/PET image reconstruction using partial differential equation (PDE) based variational framework. The aim of this paper is to impose an effective edge preserving and noise removing to optimize the quality of CT/PET reconstructed images. A comparative analysis of the proposed model with some other existing standard methods in literature is presented both qualitatively and quantitatively using simulated test phantom and standard digital image. An experimental result indicates that the proposed method yields significantly improvements in quality of reconstructed images from the projection data. The obtained results justify the applicability of the proposed method.