A lattice implementation of high-precision IIR filter for X-ray CT reconstruction

The authors previously proposed forward and backward one round (FBOR) method to accelerate the filtering process by realizing the discrete Hilbert transform (DHT) function using an IIR filter in the convolution backprojection (CB) method that is a typical reconstruction algorithm for the X-ray CT. The FBOR method cascades causal and anticausal allpass filters to realize the linear phase DHT, and implements them by parallel ladders of allpass filters. Unfortunately, this method has to adopt the DHT that has the brickwall transition at the zero frequency and thus, requires high sensitivity coefficients in order to reduce distortions of a reconstructed image. As a result, it needs to rely on double precision floating points to avoid cancellations of significant digits. In this paper, we propose a successive-scan one-round (SSOR) method of implementing the DHT by cascading primary lattice allpass filters that allows the use of single precision floating points. We confirm the effectiveness of our proposal through simulations.