Nearly all estimators in statistical prediction come with an associated tuning parameter, in one way or another. Common practice, given data, is to choose the tuning parameter value that minimizes a constructed estimate of the prediction error of the estimator; we focus on Stein’s unbiased risk estimator, or SURE (Stein, 1981; Efron, 1986), which forms an unbiased estimate of the prediction err...

We address the problem of channel estimation for cyclic-prefix (CP) Orthogonal Frequency Division Multiplexing (OFDM) systems. We model the channel as a vector of unknown deterministic constants and hence, do not require prior knowledge of the channel statistics. Since the mean-square error (MSE) is not computable in practice, in such a scenario, we propose a novel technique using Stein’s lemma...

Stein’s formula states that a random variable of the form z⊤f(z)−divf(z) is mean-zero for all functions f with integrable gradient. Here, divf divergence function and z standard normal vector. This paper aims to propose second-order Stein characterize variance such variables f(z) square gradient, demonstrate usefulness this in various applications. In Gaussian sequence model, remarkable consequ...

We address the problem of suppressing background noise from noisy speech within a risk estimation framework, where the clean signal is estimated from the noisy observations by minimizing an unbiased estimate of a chosen risk function. For Gaussian noise, such a risk estimate was derived by Stein, which eventually went on to be called Stein’s unbiased risk estimate (SURE). Stein’s formalism is r...

Algorithms to solve variational regularization of ill-posed inverse problems usually involve operators that depend on a collection of continuous parameters. When these operators enjoy some (local) regularity, these parameters can be selected using the socalled Stein Unbiased Risk Estimate (SURE). While this selection is usually performed by exhaustive search, we address in this work the problem...

Denoising is an essential step prior to any higher-level image-processing tasks such as segmentation or object tracking, because the undesirable corruption by noise is inherent to any physical acquisition device. When the measurements are performed by photosensors, one usually distinguish between two main regimes: in the first scenario, the measured intensities are sufficiently high and the noi...

Image denoising as a pre-processing stage is a used to preserve details, edges and global contrast without blurring the corrupted image. Among state-of-the-art algorithms, block shrinkage denoising is an effective and compatible method to suppress additive white Gaussian noise (AWGN). Traditional NeighShrink algorithm can remove the Gaussian noise significantly, but loses the edge information i...

We study the effective degrees of freedom of the lasso in the framework of Stein’s unbiased risk estimation (SURE). We show that the number of nonzero coefficients is an unbiased estimate for the degrees of freedom of the lasso—a conclusion that requires no special assumption on the predictors. In addition, the unbiased estimator is shown to be asymptotically consistent. With these results on h...

The goal of speech enhancement algorithms is to provide an estimate of clean speech starting from noisy observations. In general, the estimate is obtained by minimizing a chosen distortion metric. The often-employed cost is the mean-square error (MSE), which results in a Wiener-filter solution. Since the ground truth is not available in practice, the practical utility of the optimal estimators ...

This paper proposed an efficient approach to orthonormal wavelet image denoising, based on minimizing the mean square error (MSE) between the clean image and the denoised one. The key point of our approach is to use the accurate, statistically unbiased, MSE estimate—Stein’s unbiased risk estimate (SURE). One of the major advantages of this method is that; we don't have to deal with the noiseles...