PCM-TV-TFV: A Novel Two-Stage Framework for Image Reconstruction from Fourier Data
PCM-TV-TFV: A Novel Two-Stage Framework for Image Reconstruction from Fourier Data
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DOI：
10.1137/17m1130666
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发表时间：
2017-05
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通讯作者：
Weihong Guo;Guohui Song;Yue Zhang-
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作者：
Weihong Guo;Guohui Song;Yue Zhang-
我们在本文中提出了一种新颖的两阶段投影校正建模（PCM）框架，用于根据（非均匀）傅立叶测量进行图像重建。 PCM由由多尺度伽辽金方法驱动的投影阶段（P阶段）和具有边缘引导规律性的校正阶段（C阶段）组成，融合了全变分和全分数变分的优点。 P 阶段允许对感兴趣的底层图像进行连续建模。给定的测量值被投影到可以很好地表示图像的空间上。然后，我们增强了 C 阶段的重建结果，最小化了由变换域中的保真度和新颖的边缘引导规则性组成的能量函数。我们进一步开发高效的近端算法来解决相应的优化问题。一维信号和二维图像的各种数值结果也被提出来证明所提出的两阶段方法的优越性能......
We propose in this paper a novel two-stage projection correction modeling (PCM) framework for image reconstruction from (nonuniform) Fourier measurements. PCM consists of a projection stage (P-stage) motivated by the multiscale Galerkin method and a correction stage (C-stage) with an edge guided regularity fusing together the advantages of total variation and total fractional variation. The P-stage allows for continuous modeling of the underlying image of interest. The given measurements are projected onto a space in which the image is well represented. We then enhance the reconstruction result at the C-stage that minimizes an energy functional consisting of a fidelity in the transformed domain and a novel edge guided regularity. We further develop efficient proximal algorithms to solve the corresponding optimization problem. Various numerical results in both one-dimensional signals and two-dimensional images have also been presented to demonstrate the superior performance of the proposed two-stage method...