The James-Stein (JS) shrinkage estimator is a biased estimator that captures
the mean of Gaussian random vectors.While it has a desirable statistical
property of dominance over the maximum likelihood estimator (MLE) in terms of
mean squared error (MSE), not much progress has been made on extending the
estimator onto manifold-valued data.
We propose C-SURE, a novel Stein's unbiased risk estimate (SURE) of the JS
estimator on the manifold of complex-valued data with a theoretically proven
optimum over MLE. Adapting the architecture of the complex-valued SurReal
classifier, we further incorporate C-SURE into a prototype convolutional neural
network (CNN) classifier. We compare C-SURE with SurReal and a real-valued
baseline on complex-valued MSTAR and RadioML datasets.
C-SURE is more accurate and robust than SurReal, and the shrinkage estimator
is always better than MLE for the same prototype classifier. Like SurReal,
C-SURE is much smaller, outperforming the real-valued baseline on MSTAR
(RadioML) with less than 1 percent (3 percent) of the baseline size

我们提出了 C-SURE，这是一种新的 Stein 偏置风险估计器，用于复值数据的流型，并将其融入了卷积神经网络分类器的原型中，在复值 MSTAR 和 RadioML 数据集上表现比 SurReal 更准确和稳健

C-SURE：用于复数值深度学习的缩减估计器与样本原型分类器

C-SURE: Shrinkage Estimator and Prototype Classifier for Complex-Valued  Deep Learning

Stein's unbiased risk estimate (SURE) was proposed by Stein for the
independent, identically distributed (iid) Gaussian model in order to derive
estimates that dominate least-squares (LS). In recent years, 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 iid case which precludes many
important applications. In this paper we begin by deriving a SURE counterpart
for general, not necessarily iid 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
approach and the discrepancy method 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 performance of the resulting estimates. To address this inherent
tradeoff we propose a regularized SURE objective. Based on this design
criterion, we derive a wavelet denoising strategy that is similar in sprit to
the standard soft-threshold approach but can lead to improved MSE performance.

该论文提出了针对广泛问题的 Stein 无偏风险估计方法，扩展了 SURE 设计技术，并建议了一种基于正则化 SURE 目标的小波去噪策略，可以改善均方误差性能。