A general total variation minimization theorem for compressed sensing based interior tomography.
A general total variation minimization theorem for compressed sensing based interior tomography.
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DOI：
10.1155/2009/125871
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发表时间：
2009
影响因子：
7.6
通讯作者：
Wang G
中科院分区：
文献类型：
--
作者：
Han W;Yu H;Wang G
最近，我们发现在压缩感知框架中，如果ROI是分段常数，则可以通过总变差最小化来精确重建二维内部感兴趣区域（Yu and Wang, 2009）。本文给出了定义在任意维定域上的分段常数函数的最小化性质的一般定理。我们证明这一结果的主要数学工具是不涉及Dirac函数的泛函分析，Yu和Wang（2009）使用了启发式分析。
Recently, in the compressed sensing framework we found that a two-dimensional interior region-of-interest (ROI) can be exactly reconstructed via the total variation minimization if the ROI is piecewise constant (Yu and Wang, 2009). Here we present a general theorem charactering a minimization property for a piecewise constant function defined on a domain in any dimension. Our major mathematical tool to prove this result is functional analysis without involving the Dirac delta function, which was heuristically used by Yu and Wang (2009).