An Improved Form of Linogram Algorithm for Image Reconstruction

The implementation of the discrete ramp filter in the filtered backprojection (FBP) algorithms has been carefully investigated by Kak and Slane in Principles of Computerized Tomographic Imaging. In the linogram algorithms, however, it was rarely used in a correct way. Instead, an oversampling (zero-padding) factor of four is usually taken to reduce the dishing artifacts. We here improve the linogram algorithm by using a new strategy of weighting instead of in its original implementation. The new weighting is produced via the Fourier transform of the discrete ramp filter similar to that in Kak and Slaney. We explicitly derive the connection between the oversampling processing and the implementation of the discrete ramp filter in the spatial domain: if projection data are zero-padded to double length, with the discrete ramp filter, the effect is theoretically equivalent to zero-padding infinitely long in the original implementation; without zero-padding, the modified algorithm can obtain almost accurate reconstruction in the central part of an image. Our theoretical analysis also gives the optimal way of implementing the linogram algorithm, leading to savings in computational time and memory space. Results of theoretical analysis are validated by numerical simulations.