ABSTRACT Limited data CT Image reconstruction is a real-life problem. A Total Variation (TV) l1 norm minimization technique has been examined and validated here to reconstruct CT images from limited data incorporating a limited number of views along with limited angular span, a situation typical in engineering applications. The Lagrangian technique has been used to solve TV equations. The reconstructed CT image has been compared with the images reconstructed by SIRT, Higher Order TV (HOTV) technique, l2 norm minimization based technique and some other techniques with the help of various image quality index (IQI) parameters. The comparison shows that the proposed scheme is an attractive solution for limited data CT Image reconstruction from industrial and engineering perspective. The application of Sobolev space error analysis has also been given to ensure good global reconstruction.

中文翻译：

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Total Variation (TV) l1 基于范数最小化的有限数据 X 射线 CT 图像重建

摘要 有限数据 CT 图像重建是一个现实生活中的问题。这里已经检查并验证了总变异 (TV) l1 范数最小化技术，以从包含有限数量视图和有限角度跨度的有限数据重建 CT 图像，这是工程应用中的典型情况。拉格朗日技术已被用于求解 TV 方程。借助各种图像质量指数（IQI）参数，将重建的 CT 图像与通过 SIRT、高阶电视（HOTV）技术、基于 l2 范数最小化技术和其他一些技术重建的图像进行了比较。比较表明，从工业和工程角度来看，所提出的方案是有限数据 CT 图像重建的有吸引力的解决方案。