Projection-Wise Filter Optimization for Limited-Angle Cone-Beam CT Using the Approximate Inverse

In this paper, we present a novel and efficient approach for the optimization of filters for limited-angle cone beam computed tomography (CBCT). Our method is based on the theory of approximate inverse (AI) and uses a simultaneous iterative reconstruction technique (SIRT) to estimate a view-dependent reconstruction kernel. From this kernel we then derive a set of 2-D filters that can be applied in a filtered backprojection (FBP) algorithm. By construction the resulting filters are independent of the measured data, so that they can be precomputed for a given geometric setup and be reused with different projection datasets. Our approach is the first application of the AI for 3-D limited-angle CBCT supported by iterative reconstruction, such that in comparison to existing methods, it does not rely on additional reference measurements or on the existence of an analytical inversion formula. However, our method reaches results better than standard FBP methods. Additionally, we provide a general scheme that allows the transfer of our method to other system geometries and gives us the ability to extend it with more complex filters. We will conduct several experiments with simulated and real data where we examine the image quality of our method in comparison to standard FBP and SIRT. The results will show that our angle-optimized FBP has a higher contrast-to-artifact ratio than FBP. In addition to this, we analyze the image quality perpendicular to the in-focus plane by the use of the artifact spread function and show that our technique can be employed to reduce the amount of ghosting artifacts.