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首页> 外文期刊>IEEE Transactions on Information Theory >Optimized Wavelet Denoising for Self-Similar -Stable Processes
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Optimized Wavelet Denoising for Self-Similar -Stable Processes

机译：自相似稳定过程的优化小波降噪

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摘要

We investigate the performance of wavelet shrinkage methods for the denoising of symmetric- -stable ( ) self-similar stochastic processes corrupted by additive white Gaussian noise (AWGN), where is tied to the sparsity of the process. The wavelet transform is assumed to be orthonormal and the shrinkage function minimizes the mean-square approximation error (MMSE estimator). We derive the corresponding formula for the expected value of the averaged estimation error. We show that the predicted MMSE is a monotone function of a simple criterion that depends on the wavelet and the statistical parameters of the process. Using the calculus of variations, we then optimize this criterion to find the best performing wavelet within the extended family of Meyer wavelets, which are bandlimited. These are compared with the Daubechies wavelets, which are compactly supported in time. We find that the wavelets that are shorter in time (in particular, the Haar basis) are better suited to denoise the sparser processes (say, ), while the bandlimited ones (including the Held and Shannon wavelets) offer the best performance for , the limit corresponding to the Gaussian case (fBm) with .
机译：我们研究了小波收缩方法的性能，该方法用于对因加性高斯白噪声（AWGN）破坏的对称稳定（）自相似随机过程的去噪性，该噪声与该过程的稀疏性有关。假设小波变换是正交的，并且收缩函数使均方近似误差（MMSE估计器）最小。我们为平均估计误差的期望值导出相应的公式。我们表明，预测的MMSE是简单准则的单调函数，该准则取决于小波和过程的统计参数。然后使用变分法对准则进行优化，以在带限的Meyer小波扩展族中找到性能最佳的小波。将这些与时间得到紧凑支持的Daubechies小波进行比较。我们发现时间较短的小波（尤其是Haar基）更适合于对稀疏过程（例如）进行降噪，而带限小波（包括Held和Shannon小波）在以下条件下具有最佳性能：与对应的高斯情况（fBm）的极限。

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