A Doubly Constrained TV Algorithm for Image Reconstruction

Abstract

Purpose. The total variation (TV) minimization algorithm is an effective image reconstruction algorithm capable of accurately reconstructing images from sparse and/or noisy data. The TV model consists of two terms: a data fidelity term and a TV regularization term. Two constrained TV models, data divergence-constrained TV minimization (DDcTV) and TV-constrained data divergence minimization (TVcDM), have been successfully applied to computed tomography (CT) and electron paramagnetic resonance imaging (EPRI). In this work, we propose a new constrained TV model, a doubly constrained TV (dcTV) model, which has the potential to further improve the reconstruction accuracy for the two terms which are both of constraint forms. Methods. We perform an inverse crime study to validate the model and its Chambolle-Pock (CP) solver and characterize the performance of the dcTV-CP algorithm in the context of CT. To demonstrate the superiority of the dcTV model, we compare the convergence rate and the reconstruction accuracy with the DDcTV and TVcDM models via simulated data. Results and Conclusions. The performance-characterizing study shows that the dcTV-CP algorithm is an accurate and convergent algorithm, with the model parameters impacting the reconstruction accuracy and the algorithm parameters impacting the convergence path and rate. The comparison studies show that the dcTV-CP algorithm has a relatively fast convergence rate and can achieve higher reconstruction accuracy from sparse projections or noisy projections relative to the other two single-constrained TV models. The knowledge and insights gained in the work may be utilized in the application of the new model in other imaging modalities including divergence-beam CT, magnetic resonance imaging (MRI), positron emission tomography (PET), and EPRI.