Filtragem de ruído em imagens tomográficas com baixa taxa de contagem utilizando uma abordagem bayesiana contextual

Abstract

Computed Tomography (CT) images, in many cases, need to be acquired with low photon counting due to low exposure time to the rays of the CT scanner to reduce the radiation doses to the maximum possible (in Medicine, the ALARA principle As Low As Reasonably Achievable) or even for reasons of cost, obtaining projections corrupted by Poisson noise. Invoking the Central Limit Theorem, the reconstructed images tend to be corrupted by Gaussian noise. Moreover, it was observed that this noise remains signal-dependent after the reconstruction. Thus, this work proposes to denoise the reconstructed images (post-filtering), by adopting an a priori contextual model by using Markov Random Field (MRF), to improve the visual quality of the image. Basically, for contextual filtering two approaches were considered. One uses iterative algorithms for combinatorial optimization such as ICM (Iterated Conditional Modes), GSA (Game Strategy Approach) and MPM (Maximizer of the Posterior Marginals). And the other uses variations of the Wiener filter by considering Fisher Information, Separable MRF and Isotropic MRF. Also, to address the issue of signal-dependent noise, three new methods for its local variance estimation, as well as ways to consider this model in both iterative and those based on Wiener filter methods were investigated. The proposed methods were applied to simulated and real CT images that were reconstructed by Filtered Backprojection (FBP) and Projections Onto Convex Sets (POCS) algorithms. Furthermore, the use of Non Local Means method has been proposed for a better estimate of the noise-free image. Finally, several experiments were conducted and the results were compiled and presented comparing the various methods, including the state-of-the-art Non Local Means method, showing that the context and the consideration of signal-dependent noise can contribute to CT denoising by improving the Signal-to-Noise Ratio and therefore allow a reduction in the radiation dose.