Fundamentals of statistical signal processing: estimation theory
Fundamentals of statistical signal processing: estimation theory
The use of the L-curve in the regularization of discrete ill-posed problems
SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
Deblurring Images: Matrices, Spectra, and Filtering (Fundamentals of Algorithms 3) (Fundamentals of Algorithms)
Robust mean-squared error estimation in the presence of model uncertainties
IEEE Transactions on Signal Processing
IEEE Transactions on Information Theory
Bayesian and regularization methods for hyperparameter estimation in image restoration
IEEE Transactions on Image Processing
Building robust wavelet estimators for multicomponent images using Stein's principle
IEEE Transactions on Image Processing
A New SURE Approach to Image Denoising: Interscale Orthonormal Wavelet Thresholding
IEEE Transactions on Image Processing
Rethinking Biased Estimation: Improving Maximum Likelihood and the Cramér–Rao Bound
Foundations and Trends in Signal Processing
A SURE approach for digital signal/image deconvolution problems
IEEE Transactions on Signal Processing
Covariance estimation in decomposable Gaussian graphical models
IEEE Transactions on Signal Processing
Nonparametric cepstrum estimation via optimal risk smoothing
IEEE Transactions on Signal Processing
Least squares estimation without priors or supervision
Neural Computation
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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 applicatious. 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 desigu 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.