Generalized row-action methods for tomographic imaging

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• 作者：Martin S. Andersen (1)
  Per Christian Hansen (1)
  
• 关键词：Incremental methods ; Proximal methods ; Inverse problems ; Regularization ; Tomographic imaging ; 65R32 ; 90C52 ; 65K05
• 刊名：Numerical Algorithms
• 出版年：2014
• 出版时间：September 2014
• 年：2014
• 卷：67
• 期：1
• 页码：121-144
• 全文大小：1,114 KB
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• 作者单位：Martin S. Andersen (1)
  Per Christian Hansen (1)
  
  1. Department of Applied Mathematics and Computer Science, Technical University of Denmark, Lyngby, Denmark
  
• ISSN：1572-9265

文摘

Row-action methods play an important role in tomographic image reconstruction. Many such methods can be viewed as incremental gradient methods for minimizing a sum of a large number of convex functions, and despite their relatively poor global rate of convergence, these methods often exhibit fast initial convergence which is desirable in applications where a low-accuracy solution is acceptable. In this paper, we propose relaxed variants of a class of incremental proximal gradient methods, and these variants generalize many existing row-action methods for tomographic imaging. Moreover, they allow us to derive new incremental algorithms for tomographic imaging that incorporate different types of prior information via regularization. We demonstrate the efficacy of the approach with some numerical examples.