The challenge of computed tomography is to reconstruct high-quality images from few-view projections. Using a prior guidance image, guided image filtering smoothes images while preserving edge features. The prior guidance image can be incorporated into the image reconstruction process to improve image quality. We propose a new simultaneous algebraic reconstruction technique based on guided image filtering. Specifically, the prior guidance image is updated in the image reconstruction process, merging information iteratively. To validate the algorithm practicality and efficiency, experiments were performed with numerical phantom projection data and real projection data. The results demonstrate that the proposed method is effective and efficient for nondestructive testing and rock mechanics.
The Landweber iteration is a general method for the solution of linear systems which is widely applied for image reconstructions. The convergence behavior of the Landweber iteration is of both theoretical and practical importance. By the representation of the iterative formula and the convergence results of the Landweber iteration, we derive the optimal relaxation method under the minimization of the spectral radius of the newly derived iterative matrix. We also establish the iterative relaxation strategy to accelerate the convergence for the Landweber iteration when only the biggest singular value is available. As an immediate result, we derive the corresponding results for the Richardson's iteration for the symmetric nonnegative definite linear systems. Finally, numerical simulations are conducted to validate the theoretical results. The advantage of the proposed relaxation strategies is demonstrated by comparing with the existing strategies.
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