TVR-DART: A More Robust Algorithm for Discrete Tomography From Limited Projection Data With Automated Gray Value Estimation

• Published in: IEEE transactions on image processing Vol. 25; no. 1; pp. 455 - 468
• Main Authors: Xiaodong Zhuge, Palenstijn, Willem Jan, Batenburg, Kees Joost
• Format: Journal Article
• Language: English
• Published: United States IEEE 01.01.2016
• Subjects: Algebra; Algorithms; Automation; compressive sensing; Computed tomography; Discrete tomography; Image processing; Image reconstruction; Image segmentation; Imaging; Linear programming; Optimization; prior knowledge; Reconstruction; Reconstruction algorithms; sparse reconstruction; Tomography; Total variation; Tuning; Discrete tomography; total variation; image reconstruction; sparse reconstruction; prior knowledge; compressive sensing
• ISSN: 1057-7149; 1941-0042; 1941-0042
• DOI: 10.1109/TIP.2015.2504869

In this paper, we present a novel iterative reconstruction algorithm for discrete tomography (DT) named total variation regularized discrete algebraic reconstruction technique (TVR-DART) with automated gray value estimation. This algorithm is more robust and automated than the original DART algorithm, and is aimed at imaging of objects consisting of only a few different material compositions, each corresponding to a different gray value in the reconstruction. By exploiting two types of prior knowledge of the scanned object simultaneously, TVR-DART solves the discrete reconstruction problem within an optimization framework inspired by compressive sensing to steer the current reconstruction toward a solution with the specified number of discrete gray values. The gray values and the thresholds are estimated as the reconstruction improves through iterations. Extensive experiments from simulated data, experimental μCT, and electron tomography data sets show that TVR-DART is capable of providing more accurate reconstruction than existing algorithms under noisy conditions from a small number of projection images and/or from a small angular range. Furthermore, the new algorithm requires less effort on parameter tuning compared with the original DART algorithm. With TVR-DART, we aim to provide the tomography society with an easy-to-use and robust algorithm for DT.