Approximate algorithms for 2N+1 sources cone-beam CT along saddle trajectories

This paper presents approximate reconstruction methods for cone-beam CT with saddle scanning loci. The 2N+1 x-ray sources and their corresponding 2N+1 detectors are symmetrically placed around the circle with radius much larger than the object. They are moving along the 2N+1 saddle trajectories respectively and the projection data are collected by corresponding detectors. Two approximate algorithms are proposed. One is the full-scan algorithm which consists of three steps: a) cone-beam data to fan-beam data conversion via a cosine correction; b) one-dimensional convolution with S-L kernel or R-L kernel along the u-axis in a local coordinate on the detector; c) three-dimensional backprojection of the filtered data. The other is super-short-scan algorithm which consists of four steps: a) cone-beam data to fan-beam data conversion via a cosine correction; b) derivative of the fan-beam data; c) Hilbert transform along the u-axis in a local coordinate on the detector; d) multiply the filtered data with a weighting function and then backproject it to the reconstructed image. The weighting function is decided by the number of x-ray sources and the starting and ending angle of each source. Although these two algorithms both have a Feldkamp-type reconstruction procedure, the super-short-scan algorithm requires less restriction of the data sufficiency condition and it can be used for region of interest imaging.