Parameter choice is crucial to regularization-based image deblurring. In this paper, a Monte Carlo method is used to approximate the optimal regularization parameter in the sense of Stein’s unbiased risk estimate (SURE) which has been applied to image deblurring. The proposed algorithm is suitable for the exact deblurring functions as well as those of not being expressed analytically. We justif...

This paper is about extending the classical Non-Local Means (NLM) denoising algorithm using general shapes instead of square patches. The use of various shapes enables to adapt to the local geometry of the image while looking for pattern redundancies. A fast FFT-based algorithm is proposed to compute the NLM with arbitrary shapes. The local combination of the different shapes relies on Stein’s ...

The contourlet transform has the benefit of efficiently capturing the oriented geometrical structures of images. In this paper, by incorporating the ideas of Stein’s Unbiased Risk Estimator (SURE) approach in Nonsubsampled Contourlet Transform (NSCT) domain, a new image denoising technique is devised. We utilize the characteristics of NSCT coefficients in high and low subbands and apply SURE sh...

Projections onto convex sets (POCS) algorithms have been widely used for image restoration problem. However, the relaxation parameter (l ) of POCS is strongly data-dependent and difficult to tune. In this work we focus on optimally selecting such parameter in POCS algorithm for image restoration. A stein’s unbiased risk estimate (SURE) based POCS (SPOCS) for image restoration algorithm is propo...

Using integration by parts on Gaussian space we construct a Stein Unbiased Risk Estimator (SURE) for the drift of Gaussian processes, based on their local and occupation times. By almost-sure minimization of the SURE risk of shrinkage estimators we derive an estimation and de-noising procedure for an input signal perturbed by a continuous-time Gaussian noise.

Towards an unbiased estimate of fluctuations in reef abundance and volume during the Phanerozoic W. Kiessling Museum of Natural History, Humboldt-University Berlin, Invalidenstr. 43, 10115 Berlin, Germany Received: 17 August 2005 – Accepted: 8 September 2005 – Published: 22 September 2005 Correspondence to: W. Kiessling ([email protected]) © 2005 Author(s). This work is lic...

We construct an estimation and de-noising procedure for an input signal perturbed by a continuous-time Gaussian noise, using the local and occupation times of Gaussian processes. The method relies on the almost-sure minimization of a Stein Unbiased Risk Estimator (SURE) obtained through integration by parts on Gaussian space, and applied to shrinkage estimators which are constructed by soft and...

The main contribution of this paper is to propose an iterative procedure for tubular structure segmentation of 2D images, which combines tight frame of Curvelet transforms with a SURE technique thresholding which is based on principle obtained by minimizing Stein Unbiased Risk Estimate for denoising. This proposed algorithm is mainly based on the TFA proposal presented in [1, 9], which we use e...

Bandable covariance matrices are often used to model the dependence structure of variables that follow a nature order. It has been shown that the tapering covariance estimator attains the optimal minimax rates of convergence for estimating large bandable covariance matrices. The estimation risk critically depends on the choice of the tapering parameter.We develop a Stein’s Unbiased Risk Estimat...

Both theoretical analysis and empirical evidence confirm that the approximate message passing (AMP) algorithm can be interpreted as recursively solving a signal denoising problem: at each AMP iteration, one observes a Gaussian noise perturbed original signal. Retrieving the signal amounts to a successive noise cancellation until the noise variance decreases to a satisfactory level. In this pape...