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首页> 外文期刊>Statistica neerlandica >Wavelet thresholding for some classes of non–Gaussian noise
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Wavelet thresholding for some classes of non–Gaussian noise

机译：某些非高斯噪声的小波阈值

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Wavelet shrinkage and thresholding methods constitute a powerful way to carry out signal denoising, especially when the underlying signal has a sparse wavelet representation. They are computationally fast, and automatically adapt to the smoothness of the signal to be estimated. Nearly minimax properties for simple threshold estimators over a large class of function spaces and for a wide range of loss functions were established in a series of papers by Donoho and Johnstone. The notion behind these wavelet methods is that the unknown function is well approximated by a function with a relatively small proportion of nonzero wavelet coefficients. In this paper, we propose a framework in which this notion of sparseness can be naturally expressed by a Bayesian model for the wavelet coefficients of the underlying signal. Our Bayesian formulation is grounded on the empirical observation that the wavelet coefficients can be summarized adequately by exponential power prior distributions and allows us to establish close connections between wavelet thresholding techniques and Maximum A Posteriori estimation for two classes of noise distributions including heavy–tailed noises. We prove that a great variety of thresholding rules are derived from these MAP criteria. Simulation examples are presented to substantiate the proposed approach.
机译：小波收缩和阈值化方法是执行信号去噪的有效方法，尤其是当基础信号具有稀疏小波表示时。它们计算速度快，并且自动适应要估计的信号的平滑度。在Donoho和Johnstone的一系列论文中，为大型函数空间上的简单阈值估计器和广泛的损失函数建立了接近极小极大的性质。这些小波方法背后的概念是，未知函数可以由具有相对较小比例的非零小波系数的函数很好地近似。在本文中，我们提出了一个框架，其中稀疏概念可以通过贝叶斯模型自然表达出来，用于基础信号的小波系数。我们的贝叶斯公式是建立在以下经验观察基础上的：小波系数可以通过指数幂先验分布进行适当总结，并允许我们在两类噪声分布（包括重尾噪声）的小波阈值化技术和最大后验估计之间建立紧密的联系。我们证明了从这些MAP标准中衍生出各种各样的阈值规则。给出了仿真示例，以证实所提出的方法。

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