Generalized SURE for Exponential Families: Applications to Regularization
Generalized SURE for Exponential Families: Applications to Regularization
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DOI：
10.1109/tsp.2008.2008212
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发表时间：
2009-02-01
影响因子：
5.4
通讯作者：
Eldar, Yonina C.
中科院分区：
文献类型：
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作者：
Eldar, Yonina C.
Stein's unbiased risk estimate （SURE）是Stein针对独立同分布（independent, idendistributed, i.i.d）提出的。高斯模型，以得出支配最小二乘（LS）的估计。最近，SURE准则被用于各种去噪问题中，用于选择使均方误差（MSE）估计最小化的正则化参数。然而，它的使用仅限于身份证的情况下，排除了许多重要的应用。在本文中，我们首先从指数族中推导出一般的，不一定是i - id分布的SURE对应物。这使得可以将SURE设计技术扩展到更广泛的问题类别。在此基础上，我们提出了一种选择惩罚LS估计正则化参数的新方法。然后，我们证明了它在图像去模糊和反卷积方面优于传统的广义交叉验证和差异方法。SURE技术也可用于设计估算，而无需预先定义其结构。然而，允许太多的自由参数会损害估计的性能。为了解决这种固有的权衡，我们提出了一个正则化的SURE目标，并演示了它在小波去噪背景下的使用。
Stein's unbiased risk estimate (SURE) was proposed by Stein for the independent, identically distributed (i.i.d.) Gaussian model in order to derive estimates that dominate least squares (LS). Recently, the SURE criterion has been employed in a variety of denoising problems for choosing regularization parameters that minimize an estimate of the mean-squared error (MSE). However, its use has been limited to the i.i.d. case which precludes many important applications. In this paper we begin by deriving a SURE counterpart for general, not necessarily i.i.d. distributions from the exponential family. This enables extending the SURE design technique to a much broader class of problems. Based on this generalization we suggest a new method for choosing regularization parameters in penalized LS estimators. We then demonstrate its superior performance over the conventional generalized cross validation and discrepancy approaches in the context of image deblurring and deconvolution. The SURE technique can also be used to design estimates without predefining their structure. However, allowing for too many free parameters impairs the estimate's performance. To address this inherent tradeoff, we propose a regularized SURE objective, and demonstrate its use in the context of wavelet denoising.