Most reconstruction algorithms for transmission tomography can be subdivided in two classes: variants of Filtered Backprojection (FBP) and iterative algebraic methods. Filtered backprojection is very fast and yields accurate results when a large number of projections are available, with high SNR and a full angular range. Algebraic methods require much more computation time, yet they are more flexible in dealing with limited data problems and noise. In this paper we propose an algorithm that combines the best of these two approaches: for a given linear algebraic method, a filter is computed that can be used within the FBP algorithm. The FBP reconstructions that result from using this filter strongly resemble the algebraic reconstructions and have many of their favorable properties, while the required reconstruction time is similar to standard-FBP. Based on a series of experiments, for both simulation data and experimental data, we demonstrate the merits of the proposed algorithm.

Abstract. In this paper we present a computational approach for fast approximation of nonlinear tomographic reconstruction methods by filtered backprojection methods. Algebraic reconstruction algorithms are the methods of choice in a wide range of tomographic applications, yet they require significant computation time, restricting their usefulness. We build upon recent work on the approximation of linear algebraic reconstruction methods and extend the approach to the approximation of nonlinear reconstruction methods, which are common in practice. We demonstrate that if a blueprint image is available that is sufficiently similar to the scanned object, our approach can compute reconstructions that approximate iterative nonlinear methods, yet have the same speed as filtered backprojection.

For computerized tomography (CT) imaging in (bio)medical applications, radiation dose reduction is extremely important. This can be achieved simply by reducing the number of projection images taken. In order to obtain accurate reconstructions from few projections, however, common reconstruction techniques are not sufficient. Algebraic reconstruction methods (ARMs) are often more suited, but inflict a much higher computational burden. In this work, a recently proposed method is applied to biomedical µCT, in which the benefits of ARMs are combined with the computational efficiency of the common Filtered Backprojection (FBP) algorithm. Our experimental results demonstrate that this approach yields reconstructed images highly similar to those obtained by an ARM, while maintaining the favorable computational efficiency of FBP.

Filtered Backprojection is the most widely used reconstruction method in transmission tomography. The algorithm is computationally efficient, but requires a large number of low-noise projections acquired over the full angular range to produce accurate reconstructions. Algebraic reconstruction methods on the other hand are in general more robust with respect to noise and can incorporate the available angular range in the underlying projection model. A drawback of these methods is their higher computational cost.In a recent article, we demonstrated that for linear algebraic reconstruction methods, a filter can be computed such that applying Filtered Backprojection using this filter yields reconstructions that approximate the algebraic method. In the present work, we explore a modification of this approach, where we use more than one algebraic filter in the reconstructions, each covering a different region of the reconstruction grid. We report the results of a series of experiments to determine the how well the reconstruction and approximation accuracy of this approach.