Nonparametric optimization of constrained total variation for tomography reconstruction.

Iterative algorithms based on constrained total-variation (TV) optimization are effective for the reconstruction of limited data from X-ray computed tomography (CT). Such algorithms can be executed by implementing alternative operations projection onto convex sets (POCS) on the constraints, and a gradient descent approach for TV objective minimization. To balance TV-gradient descent with POCS, the adaptive-steepest-descent (ASD) method utilizes a set of complicated parameters to adjust the TV-gradient-descent step-size. The optimal parameters are difficult for users to select, and moreover, users have to empirically choose different parameters when reconstructing different types of images. To deal with these drawbacks, this paper proposes a nonparametric method for constrained TV optimization. The method automatically updates the step-size of TV iteration according to the changes in the consistency term defined by the constraints without introducing artificial parameters. The proposed method avoids the time-consuming parameter optimization, and can be conveniently implemented in various applications. Experimental results on phantom data demonstrate the flexibility and effectiveness of the proposed method.