The constrained split Bregman algorithm for enhancing the quality of image reconstruction and analysis in few-view computed tomography

Abstract: Decreasing the scanning time by limiting the number of projection images taken in in-line computed tomography (CT) increases the ill-posedness of the algebraic reconstruction problem. Reformulating the few-view CT reconstruction problem to the total variation (TV) regularization minimization reduces the ill-posedness of the problem significantly by selecting the solution with the sparsest image gradient. The split Bregman algorithm is an efficient solver for TV regularization minimization problems. A practical version of the split Bregman algorithm minimizes the constrained TV regularization problem using the Bregman update rule bound to a priori knowledge of the noise level. This paper investigates the effect of the constrained split Bregman reconstruction algorithm in image analysis of few-view realistically simulated CT data compared to the results of few-view and full-view reconstruction of standard method and unconstrained split Bregman algorithms. Our numerical results demonstrate the few-view reconstruction of the constrained split Bregman algorithm has a smaller computation time to converge to a similar result as the few-view reconstruction of unconstrained split Bregman applying regularization parameters adapted to the noise level. Also, both iterative reconstruction algorithms perform better than the few-view reconstruction of the standard method and present results very close to the reconstruction of the standard method using sufficient projections.