Image reconstruction for positron emission tomography using fuzzy nonlinear anisotropic diffusion penalty

Abstract

Iterative algorithms such as maximum likelihood-expectation maximization (ML-EM) become the standard for the reconstruction in emission computed tomography. However, such algorithms are sensitive to noise artifacts so that the reconstruction begins to degrade when the number of iterations reaches a certain value. In this paper, we have investigated a new iterative algorithm for penalized-likelihood image reconstruction that uses the fuzzy nonlinear anisotropic diffusion (AD) as a penalty function. The proposed algorithm does not suffer from the same problem as that of ML-EM algorithm, and it converges to a low noisy solution even if the iteration number is high. The fuzzy reasoning instead of a nonnegative monotonically decreasing function was used to calculate the diffusion coefficients which control the whole diffusion. Thus, the diffusion strength is controlled by fuzzy rules expressed in a linguistic form. The proposed method makes use of the advantages of fuzzy set theory in dealing with uncertain problems and nonlinear AD techniques in removing the noise as well as preserving the edges. Quantitative analysis shows that the proposed reconstruction algorithm is suitable to produce better reconstructed images when compared with ML-EM, ordered subsets EM (OS-EM), Gaussian-MAP, MRP, TV-EM reconstructed images.

A Novel Adaptive Probabilistic Nonlinear Denoising Approach for Enhancing PET Data Sinogram

“…The main drawback of the above filter, with respect to sinogram images is that the diffusion produces important oscillations in the gradient. This leads to a poorly smoothed image [11,12]. Moreover, the adopted diffusivity functions do not consider the special properties of the sinogram, which are high level of Poisson noise and curved-shape features.…”

“…However, the considered cascading approach is time consuming, and the results are highly dependent on the parameters selection criteria. Zhu et al [11] built the diffusivity function using fuzzy rules that were expressed in a linguistic form.…”