Backprojection Wiener deconvolution for computed tomographic reconstruction

Analytical CT reconstruction is popular in practice because of its computational efficiency, but it suffers from low reconstruction quality when an insufficient number of projections are used. To address this issue, this paper presents a new analytical method of backprojection Wiener deconvolution (BPWD). BPWD executes backprojection first, and then applies a Wiener deconvolution to the whole backprojected image. The Wiener filter is derived from a ramp filter, enabling the proposed approach to perform reconstruction and denoising simultaneously. The use of a filter after backprojection does not differentiate between real sampled projections and interpolated ones, introducing reconstruction errors. Therefore a weighted ramp filter was applied to increase the contribution of real sampled projections in the reconstruction, thus improving reconstruction quality. Experiments on synthetic data and real phase-contrast x-ray images showed that the proposed approach yields better reconstruction quality compared to the classical filtered backprojection (FBP) method, with comparable reconstruction speed.