Accelerated gradient methods for total-variation-based CT image reconstruction

Jakob Heide Jørgensen, Tobias Lindstrøm Jensen, Per Christian Hansen, Søren Holdt Jensen, Emil Y. Sidky, Xiaochuan Pan

    Research output: Chapter in Book/Report/Conference proceedingArticle in proceedingsResearchpeer-review


    Total-variation (TV)-based CT image reconstruction has shown experimentally to be capable of producing accurate reconstructions from sparse-view data. In particular TV-based reconstruction is very well suited for images with piecewise nearly constant regions. Computationally, however, TV-based reconstruction is much more demanding, especially for 3D imaging, and the reconstruction from clinical data sets is far from being close to real-time. This is undesirable from a clinical perspective, and thus there is an incentive to accelerate the solution of the underlying optimization problem. The TV reconstruction can in principle be found by any optimization method, but in practice the large scale of the systems arising in CT image reconstruction preclude the use of memory-demanding methods such as Newton’s method. The simple gradient method has much lower memory requirements, but exhibits slow convergence. In the present work we address the question of how to reduce the number of gradient method iterations needed to achieve a high-accuracy TV reconstruction. We consider the use of two accelerated gradient-based methods, GPBB and UPN, to solve the 3D-TV minimization problem in CT image reconstruction. The former incorporates several heuristics from the optimization literature such as Barzilai-Borwein (BB) step size selection and nonmonotone line search. The latter uses a cleverly chosen sequence of auxiliary points to achieve a better convergence rate. The methods are memory efficient and equipped with a stopping criterion to ensure that the TV reconstruction has indeed been found. An implementation of the methods (in C with interface to Matlab) is available for download from We compare the proposed methods with the standard gradient method, applied to a 3D test problem with synthetic few-view data. We find experimentally that for realistic parameters the proposed methods significantly outperform the gradient method.
    Original languageEnglish
    Title of host publicationProceedings of 11th Fully 3D Meeting
    Publication date2011
    Publication statusPublished - 2011
    Event11th International Meeting on Fully Three-Dimensional Image Reconstruction in Radiology and Nuclear Medicine - Potsdam, Germany
    Duration: 11 Jul 201115 Jul 2011
    Conference number: 11


    Conference11th International Meeting on Fully Three-Dimensional Image Reconstruction in Radiology and Nuclear Medicine
    Internet address


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