Exact recovery of the support of piecewise constant images via total variation regularization

IF 4.6 Q2 MATERIALS SCIENCE, BIOMATERIALS
Yohann De Castro, Vincent Duval and Romain Petit
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引用次数: 0

Abstract

This work is concerned with the recovery of piecewise constant images from noisy linear measurements. We study the noise robustness of a variational reconstruction method, which is based on total (gradient) variation regularization. We show that, if the unknown image is the superposition of a few simple shapes, and if a non-degenerate source condition holds, then, in the low noise regime, the reconstructed images have the same structure: they are the superposition of the same number of shapes, each a smooth deformation of one of the unknown shapes. Moreover, the reconstructed shapes and the associated intensities converge to the unknown ones as the noise goes to zero.
通过总变异正则化精确恢复片断常数图像的支持度
这项研究涉及从噪声线性测量中恢复片状常数图像。我们研究了一种基于总(梯度)变化正则化的变分重建方法的噪声鲁棒性。我们的研究表明,如果未知图像是几个简单形状的叠加,并且如果非退化源条件成立,那么在低噪声条件下,重建图像具有相同的结构:它们是相同数量形状的叠加,每个形状都是其中一个未知形状的平滑变形。此外,当噪声为零时,重建的形状和相关的强度都会趋近于未知形状。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
ACS Applied Bio Materials
ACS Applied Bio Materials Chemistry-Chemistry (all)
CiteScore
9.40
自引率
2.10%
发文量
464
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