Algebraic filter approach for fast approximation of nonlinear tomographic reconstruction methods

We present a computational approach for fast approximation of nonlinear tomographic reconstruction methods by filtered backprojection (FBP) 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 FBP

Algebraic filters for filtered backprojection

Computed Tomography (CT) is an imaging technique that is used to calculate the interior of an object using X-rays under multiple projection angles. A well-known application is medical imaging with a CT-scanner. The reconstruction methods can roughly be divided into two categories: analytical reconstruction methods and algebraic reconstruction methods (ARMs). An example of an algorithm from the first category is Filtered Backprojection (FBP). This method has a high computational efficiency and it performs well in cases with many equiangularly distributed projection angles and high signal-to-noise ratio. ARMs require in general more computation time. They are more robust with respect to noise and can handle few projection angles or a limited angular range better. In this dissertation, the new algorithm Algebraic filter – Filtered Backprojection (AF-FBP) is introduced, which uses an ARM to create filters that can be used in FBP. The reconstruction quality of AF-FBP approximates that of the corresponding (locally) linear ARM, while the reconstructions are obtained with the computational efficiency of FBP. In cases with a small number of different scanning geometries, using AF-FBP enables the reconstruction of images of relatively high quality for few projection angles, limited angular range, or low signal-to-noise ratio.Number theory, Algebra and Geometr