Penalized weighted least-squares approach to sinogram noise reduction and image reconstruction for low-dose X-ray computed tomography

Reconstructing low-dose X-ray computed tomography (CT) images is a noise problem. This work investigated a penalized weighted least-squares (PWLS) approach to address this problem in two dimensions, where the WLS considers first-and second-order noise moments and the penalty models signal spatial correlations. Three different implementations were studied for the PWLS minimization. One utilizes a Markov random field (MRF) Gibbs functional to consider spatial correlations among nearby detector bins and projection views in sinogram space and minimizes the PWLS cost function by iterative Gauss-Seidel algorithm. Another employs Karhunen-Loève (KL) transform to de-correlate data signals among nearby views and minimizes the PWLS adaptively to each KL component by analytical calculation, where the spatial correlation among nearby bins is modeled - by the same Gibbs functional. The third one models the spatial correlations among image pixels in image domain also by a MRF Gibbs functional and minimizes the PWLS by iterative successive over-relaxation algorithm. In these three implementations, a quadratic functional regularization was chosen for the MRF model. Phantom experiments showed a comparable performance of these three PWLS-based methods in terms of suppressing noise-induced streak artifacts and preserving resolution in the reconstructed images. Computer simulations concurred with the phantom experiments in terms of noise-resolution tradeoff and detectability in low contrast environment. The KL-PWLS implementation may have the advantage in terms of computation for high-resolution dynamic low-dose CT imaging.