Pareto frontier analysis of spatio-temporal total-variation based four-dimensional cone-beam CT

Abstract

Compressed sensing (CS) based four dimensional (4D) cone-beam (CB) computed tomography (CT) reconstruction intrinsically is a multi-objective optimization problem. In practice, however, often a heuristically chosen single objective cost function is minimized. In this paper Pareto-frontier analysis was utilized to explore the image quality of the multi-objective solution space. The 4D-CBCT CS reconstruction was solved as an unconstrained optimization problem with the objective function consisting of data fidelity, spatial sparsity term (with regularization parameter λ) and temporal sparsity term (with regularization parameter β). Data fidelity was defined by an l2-norm term and the sparsity was extracted by the total-variation (TV) norm. The Pareto front was explored for a large range of λ and β parameter combinations optimized using Neterov’s descent method. Image quality was evaluated using correlation ratio (CR), mutual information (MI), structural similarity index (SSI), and contrast-to-noise ratio (CNR) on both phantom and clinical data. Higher image quality metrics were obtained with the CS optimized 4D-CBCT compared to Feldkamp (FDK) reconstructed 4D-CBCT. The optimal parameter values, however, were distinctly different for the different image quality metrics, scans and regions-of-interest. For the phantom data, the optimized CBCT have similar numerical results by CR and MI, but the results differ for SSI. For clinical data, it was found that kept the CS CBCT with 15% difference to the CBCT of optimal CNR. The optimal regularization parameter values in CS optimized 4D-CBCT were found to be patient and image quality metric dependent. The regularization should therefore be tailored to specific clinical applications.