A fast image reconstruction method for planar objects CT inspired by differentiation property of Fourier transform (DPFT)

Abstract

In planar objects computed tomography (CT), restricted to the scanning environment, projections can only be collected from limited angles. Moreover, limited by the emitting power of the x-ray source, only a few photons penetrate the long side of the planar objects, which results in the noise increasing in projections. Planar objects CT reconstruction based on these two conditions is mathematically corresponding to solving an ill-posed inverse problem. Although several iterative reconstruction algorithms of limited-angle CT were proposed, high-quality planar objects CT reconstruction algorithms with fast convergence are still the goals of many researchers. In order to address the aforementioned problems, we proposed a new optimization model for planar objects CT reconstruction. Inspired by the theory of ‘visible boundary and invisible boundary’ in limited-angle CT and the differentiation property of Fourier transform, a new optimization objective function is proposed in this paper. Based on the statistical noise model of existing CT system, the convex set constraint of the optimization model is given. Besides, the optimization model is solved by convex set projection and Fourier transform differentiation property. The proposed algorithm was evaluated with both simulated data and real data. The experimental results show that the proposed algorithm can achieve the effect of noise suppression, limited-angle artifacts reduction, and fast structure reconstruction when it applies to planar objects CT.