Nowadays, positron emission tomography (PET) is widely used in engineering. In this paper, a novel penalized maximum likelihood (PML) algorithm is presented for improving the quality of PET images. The proposed algorithm fuses an anisotropic median-diffusion (AMD) filter to the maximum-likelihood expectation-maximization (MLEM) algorithm. The fusing algorithm shows its positive effect on image reconstruction and denoising. Experimental results present that the proposed method denoises and reconstructs images with high quality. Furthermore, by comparing with other classical reconstructing algorithms, this novel algorithm shows better performance in the edge preservation. 1. Introduction PET technology, which has been widely used in neurology, oncology, and new medicine exploitation, is one of the advanced and noninvasive diagnostic techniques in modern nuclear medical. In order to obtain a high quality reconstructed image from clinical projection data with strong noise, an excellent image reconstruction algorithm is indispensable. The MLEM algorithm is a classic method in PET image reconstruction when the measured data follows Poisson distribution [1]. One problem of this algorithm is the ill-posed problem, which represents that the reconstructed images cannot remove the noise of projection data [2]. Today, an ill-posed image reconstruction problem, such as MLEM, can be transformed into a well-posed one through the use of regularization term. The reconstructed results should be not only content with measured data to some extent but also be consistent with additional regularization term that is independent of those data at the same time. That is usually called PML or Bayesian algorithm. Numerous PML algorithms have been proposed in the past decades [3–10]. Thereinto, Green proposed a Bayesian algorithm, known as the one-step-late (OSL) algorithm [6]. The key of this algorithm is to find an appropriate energy function, which is defined by Gibbs probability distribution. Unfortunately, the selection of the energy function is difficult. The median root prior (MRP) algorithm [9], firstly proposed by Alenius, is an application of OSL algorithm. This algorithm is good at coping with those images that have locally monotonic structures. However, the images reconstructed by MRP are still noisy because median filter cannot remove Gaussian and Poisson noise effectively, which dominate in PET images [7]. The anisotropic diffusion (AD) filter [11] is a nonlinear partial differential equation (PDE) based on diffusion process. Overcoming the undesirable effects of
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