Infinite impulse response filtering for cone beam tomography

In computed tomography (CT) or conebeam tomography (CBT), filtered backprojection (FBP) has been known as an efficient technique for reconstructing 3D-volumes from acquired projection data. Plain backprojection only would result in systematically blurred objects. To compensate for this blurring, convolution-based filters have been derived that are non-local and sampled with 2048 coefficients or more, dependent on the projection data size. This filtering operation can be classified as finite impulse response (FIR) filtering. In terms of image quality, ideally-derived kernels sometimes amplify too much the high frequency noise (e.g. due to X-ray quantum noise) from the input projections. In practice, regularized filters are often preferred, damping higher frequencies while preserving the sharpness and signal dynamics needed for the reconstructed 3D-objects. From discrete systems theory, another filter type with infinite impulse response (IIR) has been known. Because such a filter recursively uses backward components, it requires very few coefficients while the long-range filter effect is preserved. In the presented work, IIR filters have systematically been designed and tested. They have been adjusted for the correction of a blurring system transfer function as well as for high-frequency noise suppression. Image quality has carefully been inspected by reconstruction of phantom data and clinical cases. It has been found that the filtering step in CBT/FBP can be realized as a recursive filter only, i.e. in self-contained IIR-notation, including adaptions like e.g. apodisation. The number of filtering operations is significantly reduced hereby. So with IIR filtering an efficient alternative for FBP filtering is available.