BACKGROUND: Ultra-limited-angle image reconstruction problem with a limited-angle scanning range less than or equal to π 2 is severely ill-posed. Due to the considerably large condition number of a linear system for image reconstruction, it is extremely challenging to generate a valid reconstructed image by traditional iterative reconstruction algorithms. OBJECTIVE: To develop and test a valid ultra-limited-angle CT image reconstruction algorithm. METHODS: We propose a new optimized reconstruction model and Reweighted Alternating Edge-preserving Diffusion and Smoothing algorithm in which a reweighted method of improving the condition number is incorporated into the idea of AEDS image reconstruction algorithm. The AEDS algorithm utilizes the property of image sparsity to improve partially the results. In experiments, the different algorithms (the Pre-Landweber, AEDS algorithms and our algorithm) are used to reconstruct the Shepp-Logan phantom from the simulated projection data with noises and the flat object with a large ratio between length and width from the real projection data. PSNR and SSIM are used as the quantitative indices to evaluate quality of reconstructed images. RESULTS: Experiment results showed that for simulated projection data, our algorithm improves PSNR and SSIM from 22.46db to 39.38db and from 0.71 to 0.96, respectively. For real projection data, our algorithm yields the highest PSNR and SSIM of 30.89db and 0.88, which obtains a valid reconstructed result. CONCLUSIONS: Our algorithm successfully combines the merits of several image processing and reconstruction algorithms. Thus, our new algorithm outperforms significantly other two algorithms and is valid for ultra-limited-angle CT image reconstruction.
Image reconstruction in phase-contrast tomography exploiting the second-order statistical properties of the projection data
