Publication date: 08/08/2019

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Summary: In X-ray tomography image reconstruction, one of the most successful approaches involves a statistical modeling with l2 norm function for fidelity regularized by a functional with lp norm, 1 < p < 2, with p &#8712; R. Among them stands out, for its results and computational performance, a technique that reconstructs an image by alternating minimization for (i) solving the l2 norm fidelity term by Simultaneous Algebraic Reconstruction Technique (SART) and (ii) constraining the regularization term, defined by a Discrete Gradient Transform (DGT) sparse transformation, using Total Variation (TV) inimization. This work proposes an improvement to the reconstruction process by adding a Bilateral Edgepreserving (BEP) regularization term to the objective function, resulting in a three-step method. BEP is a noise reduction framework and has the purpose of adaptively eliminating noise in the initial phase of reconstruction process. BEP improves optimization of the fidelity term and, as a consequence, improves the result of DGT minimization by total variation. Regular dosage experiments shown favorable results compared to classical methods, such as Filtred Backprojection (FBP), and more modern ones, such as l2 norm optimization by using SART, and the l2 norm SART solution regularized by l1 norm TV optimization of DGT (SART+DGT), especially with the Structural Similarity Index Measurement (SSIM) metric. Although not so prominent in the case of regular dosing reconstruction, Peak Signal-to-noise Ratio (PSNR) results are consistent with those of SSIM. For low dosage, the quality of the reconstruction worsens for all methods, but is markedly lower for the FBP and SART methods. In this context of limited number of projections (low dosage), the reconstructions with the method here proposed presents better defined edges, in addition to better contrast and less artifacts in surfaces of regular
intensity (low intensity variation). These results are generally obtained with a smaller number of steps compared to the other iterative methods implemented in this Thesis. However, this behavior (of the proposed method) depends on the parameterization of the lp norm, 1 &#8804; p &#8804; 2, used in the BEP stage. It is experimentally shown that by varying the norm during the reconstruction process it is possible to keep the proposed method stable over a sufficiently large number of iteractions. It is also graphically shown that the method
converge, meaning that the SSIM and PSNR metrics can be continuously improved by a sufficiently large number of iteractions. For reconstructions with a limited number of projections (low-dose reconstruction), the proposed method can achieve higher PSNR and SSIM results because it can better control the noise in the initial processing phase.
Keywords: Signal processing, Biomedical engineering, X-ray computed tomography,
Image reconstruction, Optimization techniques, Bilateral edge preservation

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