Optimal Filtered Backprojection for Fast and Accurate Tomography Reconstruction
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Tomographic reconstruction is a method of reconstructing a high dimensional image with a series of its low dimensional projections, and the filtered backprojection is one of very popular analytical techniques for the reconstruction due to its computational efficiency and easy of implementation. The accuracy of the filtered backprojection method deteriorates when input data are noisy or input data are available for only a limited number of projection angles. For the case, some algebraic approaches perform better, but they are based on computationally slow iterations. We propose an improvement of the filtered backprojection method which is as fast as the existing filtered backprojection and is as accurate as the algebraic approaches under heavy observation noises and limited availability of projection data. The new approach optimizes the filter of the backprojection operator to minimize a regularized reconstruction error. We compare the new approach with the state-of-the-art in the filtered backprojection and algebraic approaches using four simulated datasets to show its competitive accuracy and computing speed.
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