Asymmetric fan-beam configurations with spatially varying focal lengths and shift-variant filtering reconstruction

We present an algorithm for image reconstruction from data acquired by use of an asymmetric fan-beam configuration with a spatially varying focal length. This algorithm is a natural generalization of our previous algorithm for fan-beam computed tomography (CT) that involves shift-variant filtering, and it possesses desirable noise and numerical properties similar to those in, the previous algorithm. We performed computer simulation studies to validate and evaluate the proposed algorithm, and quantitative results demonstrate that the proposed algorithm possesses desirable noise and numerical properties. The filtered backprojection algorithm can reconstruct images from data acquired in a configuration with a constant focal length. In this situation, the proposed algorithm yields images with lower and more uniform noise properties than the filtered backprojection algorithm.