DE-NOISING BY SOFT-THRESHOLDING
DE-NOISING BY SOFT-THRESHOLDING
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DOI：
10.1109/18.382009
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发表时间：
1995-05-01
影响因子：
2.5
通讯作者：
DONOHO, DL
中科院分区：
文献类型：
--
作者：
DONOHO, DL
Donoho和Johnstone（1994）提出了一种从噪声数据d(i) = f(t(i)) + sigma z(i), i = 0，…， n - 1, t(i) = i/n，其中z(i)是独立且同分布的标准高斯随机变量，重构(f) / cap(n)*在小波域中通过将d的所有经验小波系数向0平移一个量sigma来定义。√2 log (n)/n。我们证明了关于这类估计量的两个结果，[Smooth]：在各种光滑度量中，[Adapt]以高概率(f)在cap(n)*上至少与f一样光滑；估计量的均方接近于f，几乎是任何可测量的估计量，均匀地在两个光滑类的大尺度上，这两个性质在几个方面是前所未有的，我们对这些结果的证明发展了抽象统计推断的新事实及其与最优恢复模型的联系。
Donoho and Johnstone (1994) proposed a method for reconstructing an unknown function f on [0, 1] from noisy data d(i) = f(t(i)) + sigma z(i), i = 0,..., n - 1, t(i) = i/n, where the z(i) are independent and identically distributed standard Gaussian random variables, The reconstruction (f) over cap(n)* is defined in the wavelet domain by translating all the empirical wavelet coefficients of d toward 0 by an amount sigma . root 2 log (n)/n. We prove two results about this type of estimator, [Smooth]: With high probability (f) over cap(n)* is at least as smooth as f, in any of a wide variety of smoothness measures, [Adapt]: The estimator comes nearly as close in mean square to f as any measurable estimator can come, uniformly over balls in each of two broad scales of smoothness classes, These two properties are unprecedented in several ways, Our proof of these results develops new facts about abstract statistical inference and its connection with an optimal recovery model.