Near-Optimal Spectral Filtering and Error Estimation for Solving Ill-Posed Problems
Near-Optimal Spectral Filtering and Error Estimation for Solving Ill-Posed Problems
复制标题
用于解决病态问题的近最优谱滤波和误差估计
DOI：
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发表时间：
2015
影响因子：
3.1
通讯作者：
D. O’Leary
中科院分区：
文献类型：
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作者：
Viktoria Taroudaki;D. O’Leary
我们考虑正则化方法的线性不适定问题的数值解，特别是图像去模糊，当奇异值分解（SVD）的运营商是可用的。我们假设无噪声问题满足离散皮卡德条件，并定义皮卡德参数，指数超过该指数的数据，在SVD的坐标系中表示，由噪声主导。我们建议估计皮卡德参数图形或使用标准的统计检验。有了这个参数，我们就可以估计噪声的平均值和标准差，并去除噪声分量，从而使滤波后的解决方案更加可靠。我们展示了如何计算一个接近最优的选择任何过滤器的过滤器参数。这包括截断奇异值分解（TSVD）滤波器，截断奇异分量法（TSCM）滤波器，和几个新的过滤器，我们定义，包括截断Tikhonov滤波器，Tikhonov-TSVD滤波器，Heaviside滤波器，和样条滤波器。我们展示了T…
We consider regularization methods for numerical solution of linear ill-posed problems, in particular image deblurring, when the singular value decomposition (SVD) of the operator is available. We assume that the noise-free problem satisfies the discrete Picard condition and define the Picard parameter, the index beyond which the data, expressed in the coordinate system of the SVD, are dominated by noise. We propose estimating the Picard parameter graphically or using standard statistical tests. Having this parameter available allows us to estimate the mean and standard deviation of the noise and drop noisy components, thus making filtered solutions much more reliable. We show how to compute a near-optimal choice of filter parameters for any filter. This includes the truncated SVD (TSVD) filter, the truncated singular component method (TSCM) filter, and several new filters which we define, including a truncated Tikhonov filter, a Tikhonov-TSVD filter, a Heaviside filter, and a spline filter. We show how t...