Wavelet deconvolution in a periodic setting
Wavelet deconvolution in a periodic setting
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DOI：
10.1111/j.1467-9868.2004.02056.x
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发表时间：
2004-01-01
影响因子：
5.8
通讯作者：
Raimondo, M
中科院分区：
文献类型：
--
作者：
Johnstone, IM;Kerkyacharian, G;Raimondo, M
反卷积问题自然地表示在傅立叶域中，而已知小波基中的阈值具有广泛的自适应特性。研究了一种快速傅立叶变换和快速小波变换相结合的方法，该方法可以在O{nlog（n）2}步内恢复在白色噪声中观测到的模糊函数。在周期性设置中，该方法适用于大多数反卷积问题，包括某些“boxcar”内核，其作为运动模糊的模型是重要的，但具有差的傅立叶特性。渐近理论通知调整参数的选择，并产生自适应性能的方法在广泛的一类措施的错误和类的功能。利用水下遥感模拟光探测和测距数据对该方法进行了验证。视觉和数值结果表明，竞争的方法有所改善。最后，我们的估计范式背后的理论给出了一个完整的表征的“maxiset”的方法：一组功能的方法达到一个接近最优的收敛速度的各种L-p损失函数。
Deconvolution problems are naturally represented in the Fourier domain, whereas thresholding in wavelet bases is known to have broad adaptivity properties. We study a method which combines both fast Fourier and fast wavelet transforms and can recover a blurred function observed in white noise with O{n log(n)2} steps. In the periodic setting, the method applies to most deconvolution problems, including certain 'boxcar' kernels, which are important as a model of motion blur, but having poor Fourier characteristics. Asymptotic theory informs the choice of tuning parameters and yields adaptivity properties for the method over a wide class of measures of error and classes of function. The method is tested on simulated light detection and ranging data suggested by underwater remote sensing. Both visual and numerical results show an improvement over competing approaches. Finally, the theory behind our estimation paradigm gives a complete characterization of the 'maxiset' of the method: the set of functions where the method attains a near optimal rate of convergence for a variety of L-p loss functions.