Numerical recipes in FORTRAN (2nd ed.): the art of scientific computing
Numerical recipes in FORTRAN (2nd ed.): the art of scientific computing
Nonlinear total variation based noise removal algorithms
Proceedings of the eleventh annual international conference of the Center for Nonlinear Studies on Experimental mathematics : computational issues in nonlinear science: computational issues in nonlinear science
Blind separation of sources using higher-order cumulants
Signal Processing
A Variational Approach to Maximum a Posteriori Estimation for Image Denoising
EMMCVPR '01 Proceedings of the Third International Workshop on Energy Minimization Methods in Computer Vision and Pattern Recognition
A Non-Local Algorithm for Image Denoising
CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Volume 2 - Volume 02
Blind separation of any source distributions via high-order statistics
Signal Processing
A moment-based nonlocal-means algorithm for image denoising
Information Processing Letters
The Split Bregman Method for L1-Regularized Problems
SIAM Journal on Imaging Sciences
A blind source separation technique using second-order statistics
IEEE Transactions on Signal Processing
Optimal Inversion of the Anscombe Transformation in Low-Count Poisson Image Denoising
IEEE Transactions on Image Processing
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A standard approach for deducing a variational denoising method is the maximum a posteriori strategy. Here, the denoising result is chosen in such a way that it maximizes the conditional distribution function of the reconstruction given its observed noisy version. Unfortunately, this approach does not imply that the empirical distribution of the reconstructed noise components follows the statistics of the assumed noise model. In this paper, we show for additive noise models how to overcome this drawback by applying an additional transformation to the random vector modeling the noise. This transformation is then incorporated into the standard denoising approach and leads to a more sophisticated data fidelity term, which forces the removed noise components to have the desired statistical properties. The good properties of our new approach are demonstrated for additive Gaussian noise by numerical examples. Our method shows to be especially well suited for data containing high frequency structures, where other denoising methods which assume a certain smoothness of the signal fail to restore the small structures.