A closed-form nonparametric Bayesian estimator in the wavelet domain of images using an approximate α-stable prior

Iterative Bayesian denoising based on variance stabilization using Contourlet Transform with Sharp Frequency Localization: application to EFTEM images

Background

Due to the presence of high noise level in tomographic series of energy filtered transmission electron microscopy (EFTEM) images, alignment and 3D reconstruction steps become so difficult. To improve the alignment process which will in turn allow a more accurate and better three dimensional tomography reconstructions, a preprocessing step should be applied to the EFTEM data series.

Results

Experiments with real EFTEM data series at low SNR, show the feasibility and the accuracy of the proposed denoising approach being competitive with the best existing methods for Poisson image denoising. The effectiveness of the proposed denoising approach is thanks to the use of a nonparametric Bayesian estimation in the Contourlet Transform with Sharp Frequency Localization Domain (CTSD) and variance stabilizing transformation (VST). Furthermore, the optimal inverse Anscome transformation to obtain the final estimate of the denoised images, has allowed an accurate tomography reconstruction.

Conclusion

The proposed approach provides qualitative information on the 3D distribution of individual chemical elements on the considered sample.

A Novel Directionlet-Based Image Denoising Method Using MMSE Estimator and Laplacian Mixture Distribution

A novel method based on directionlet transform is proposed for image denoising under Bayesian framework. In order to achieve noise removal, the directionlet coefficients of the uncorrupted image are modeled independently and identically by a two-state Laplacian mixture model with zero mean. The expectation-maximization algorithm is used to estimate the parameters that characterize the assumed prior model. Within the framework of Bayesian theory, the directionlet coefficients of noise-free image are estimated by a nonlinear shrinkage function based on weighted average of the minimum mean square error estimator. We demonstrate through simulations with images contaminated by additive white Gaussian noise that the proposed method is very competitive when compared with other methods in terms of both peak signal-to-noise ratio and visual quality.

An Extension of the Interscale SURE-LET Approach for Image Denoising

In this paper, an extension of the interscale SURE-LET approach exploiting the interscale and intrascale dependencies of wavelet coefficients is proposed to improve denoising performance. This method incorporates information on neighbouring coefficients into the linear expansion of thresholds (LETs) without additional parameters to capture the texture characteristics of this image. The resulting interscale-intrascale wavelet estimator consists of a linear expansion of multivariate thresholding functions, whose parameters are optimized thanks to a multivariate Stein's unbiased risk estimate (SURE). Some experimental results are given to demonstrate the strength of the proposed method.

Bayesian wavelet-based image denoising using the Gauss-Hermite expansion

The probability density functions (PDFs) of the wavelet coefficients play a key role in many wavelet-based image processing algorithms, such as denoising. The conventional PDFs usually have a limited number of parameters that are calculated from the first few moments only. Consequently, such PDFs cannot be made to fit very well with the empirical PDF of the wavelet coefficients of an image. As a result, the shrinkage function utilizing any of these density functions provides a substandard denoising performance. In order for the probabilistic model of the image wavelet coefficients to be able to incorporate an appropriate number of parameters that are dependent on the higher order moments, a PDF using a series expansion in terms of the Hermite polynomials that are orthogonal with respect to the standard Gaussian weight function, is introduced. A modification in the series function is introduced so that only a finite number of terms can be used to model the image wavelet coefficients, ensuring at the same time the resulting PDF to be non-negative. It is shown that the proposed PDF matches the empirical one better than some of the standard ones, such as the generalized Gaussian or Bessel K-form PDF. A Bayesian image denoising technique is then proposed, wherein the new PDF is exploited to statistically model the subband as well as the local neighboring image wavelet coefficients. Experimental results on several test images demonstrate that the proposed denoising method, both in the subband-adaptive and locally adaptive conditions, provides a performance better than that of most of the methods that use PDFs with limited number of parameters.