High order total variation method for interior tomography

Jiansheng Yang; Hengyong Yu; Wenxiang Cong; Ming Jiang; Ge Wang

doi:10.1117/12.929123

17 October 2012 High order total variation method for interior tomography

Jiansheng Yang, Hengyong Yu, Wenxiang Cong, Ming Jiang, Ge Wang

Proceedings Volume 8506, Developments in X-Ray Tomography VIII; 85061B (2012) https://doi.org/10.1117/12.929123
Event: SPIE Optical Engineering + Applications, 2012, San Diego, California, United States

Abstract

While classic CT theory targets exact reconstruction of a whole cross-section or an entire object, practical applications often focus on a region of interest (ROI). The long-standing interior problem is well known that an internal ROI cannot be exactly reconstruct only from truncated projection data associated with x-rays through the ROI. Although lambda tomography was developed to target gradient-like features of an internal ROI for the interior problem, it has not been well accepted in the biomedical community. On the other hand, approximate local reconstruction methods are subject to biases and artifacts. Recently, the interior problem is re-visited with appropriate prior knowledge, delivering practical results. First, the interior problem can be exactly and stably solved if a sub-region in an ROI is known. Thereafter, the sub-region knowledge can be replaced by certain rather weak constraints. For local reconstruction, a candidate image can be represented as the sum of the truth and an ambiguity component. Very surprisingly, the ROI image is prove to be the unique minimizer of the total variation (TV) or high order total variation (HOT) functional subject to the measurement, if the ROI is piece-wise constant or polynomial. Interior tomography algorithms based on HOT minimization have been developed for x-ray CT, and then extended for interior SPECT and interior differential phasecontrast tomography, respectively. In this paper, we will summarize the main theoretical and algorithmic results.

Citation Download Citation

Jiansheng Yang, Hengyong Yu, Wenxiang Cong, Ming Jiang, and Ge Wang "High order total variation method for interior tomography", Proc. SPIE 8506, Developments in X-Ray Tomography VIII, 85061B (17 October 2012); https://doi.org/10.1117/12.929123

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