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摘要翻译：
本文研究了分段光滑函数的n次谱中的边缘检测问题，假设该函数被噪声破坏。它涉及到三个尺度：1/n阶的“光滑性”尺度、$\eta$阶的噪声尺度和跳变间断的O(1)尺度。我们使用与噪声方差($\eta$>>1/n)调整的浓度因子来检测与噪声尺度($\eta$<<1)分离的潜在O(1)-边缘。
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英文标题：
《Recovery of edges from spectral data with noise -- a new perspective》
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作者：
Shlomo Engelberg and Eitan Tadmor
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最新提交年份：
2007
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分类信息：
一级分类：Mathematics 数学
二级分类：Numerical Analysis 数值分析
分类描述：Numerical algorithms for problems in analysis and algebra, scientific computation
分析和代数问题的数值算法，科学计算
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一级分类：Mathematics 数学
二级分类：Statistics Theory 统计理论
分类描述：Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计：例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
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一级分类：Statistics 统计学
二级分类：Statistics Theory 统计理论
分类描述：stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近，贝叶斯推论，决策理论，估计，基础，推论，检验。
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英文摘要：
We consider the problem of detecting edges in piecewise smooth functions from their N-degree spectral content, which is assumed to be corrupted by noise. There are three scales involved: the "smoothness" scale of order 1/N, the noise scale of order $\eta$ and the O(1) scale of the jump discontinuities. We use concentration factors which are adjusted to the noise variance, $\eta$ >> 1/N, in order to detect the underlying O(1)-edges, which are separated from the noise scale, $\eta$ << 1.
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PDF链接：
https://arxiv.org/pdf/704.3822
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