Abstract
A variety of alternating direction methods have been proposed for solving a class of optimization problems. The applications in computed tomography (CT) perform well in image reconstruction. The reweighted schemes were applied in l1-norm and total variation minimization for signal and image recovery to improve the convergence of algorithms. In this paper, we present a reweighted total variation algorithm using the alternating direction method (ADM) for image reconstruction in CT. The numerical experiments for ADM demonstrate that adding reweighted strategy reduces the computation time effectively and improves the quality of reconstructed images as well.
Highlights
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We present a reweighted total variation algorithm using the alternating direction method (ADM) for image reconstruction in computed tomography (CT)
The reweighted total variation (TV) minimization has shown its capability of speeding up the convergence of sparse image reconstruction in CT since it was proposed more than ten years ago
Summary
We introduce notations and review approaches for solving a TV minimization problem (3) using the reweight scheme and ADM in the literature, respectively. In the case of sparse signal recovery, it is extremely important to identify the locations of nonzero entries of a sparse vector x. The idea of the reweighted l1 minimization is to make the weights small for the entries of x larger in magnitude and the weights large for those smaller in magnitude. Reweighted l1 minimization speeds up the convergence of recovery. The gradient ∇f of an essentially piecewise constant image f is sparse so a reweighted scheme could be adopted to speed up the convergence and improve the efficiency of image reconstruction. ADM iterates as f k+1 = arg min L(f, vk, λk);.
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