Improved total variation based CT reconstruction algorithm with noise estimation

Abstract

Nowadays a famous way to solve Computed Tomography (CT) inverse problems is to consider a constrained minimization problem following the Compressed Sensing (CS) theory. The CS theory proves the possibility of sparse signal recovery using under sampled measurements which gives a powerful tool for CT problems that have incomplete measurements or contain heavy noise. Among current CS reconstruction methods, one widely accepted reconstruction framework is to perform a total variation (TV) minimization process and a data fidelity constraint process in an alternative way by two separate iteration loops. However because the two processes are done independently certain misbalance may occur which leads to either over-smoothed or noisy reconstructions. Moreover, such misbalance is usually difficult to adjust as it varies according to the scanning objects and protocols. In our work we try to make good balance between the minimization and the constraint processes by estimating the variance of image noise. First, considering that the noise of projection data follows a Poisson distribution, the Anscombe transform (AT) and its inversion is utilized to calculate the unbiased variance of the projections. Second, an estimation of image noise is given through a noise transform model from projections to the image. Finally a modified CS reconstruction method is proposed which guarantees the desired variance on the reconstructed image thus prevents the block-wising or over-noised caused by misbalanced constrained minimizations. Results show the advantage in both image quality and convergence speed.