Locally adaptive multiscale Bayesian method for image denoising based on bivariate normal inverse Gaussian distributions

2007 ◽  
Author(s):  
Mohamad Forouzanfar ◽  
Hamid Abrishami Moghaddam ◽  
Sona Ghadimi
Keyword(s):  
Image Denoising ◽  
Bayesian Method ◽  
Inverse Gaussian ◽  
Gaussian Distributions ◽  
Bivariate Normal ◽  
Locally Adaptive ◽  
Normal Inverse Gaussian

LOCALLY ADAPTIVE MULTISCALE BAYESIAN METHOD FOR IMAGE DENOISING BASED ON BIVARIATE NORMAL INVERSE GAUSSIAN DISTRIBUTIONS

2008 ◽  
Vol 06 (04) ◽  
pp. 653-664 ◽  
Author(s):  
MOHAMAD FOROUZANFAR ◽  
HAMID ABRISHAMI MOGHADDAM ◽  
SONA GHADIMI
Keyword(s):  
Statistical Model ◽  
Image Denoising ◽  
Minimum Mean Square Error ◽  
Model Parameters ◽  
Inverse Gaussian ◽  
Wavelet Coefficients ◽  
Bivariate Normal ◽  
Wide Range ◽  
Heavy Tailed ◽  
Normal Inverse Gaussian

Recently, the use of wavelet transform has led to significant advances in image denoising applications. Among wavelet-based denoising approaches, the Bayesian techniques give more accurate estimates. Considering interscale dependencies, these estimates become closer to the original image. In this context, the choice of an appropriate model for wavelet coefficients is an important issue. The performance can also be improved by estimating model parameters in a local neighborhood. In this paper, we propose the bivariate normal inverse Gaussian (NIG) distribution, which can model a wide range of heavy-tailed to less heavy-tailed processes, to model the local wavelet coefficients at adjacent scales. We will show that this new statistical model is superior to the conventional generalized Gaussian (GG) model. Then, a minimum mean square error-based (MMSE-based) Bayesian estimator is designed to effectively remove noise from wavelet coefficients. Exploiting this new statistical model in the dual-tree complex wavelet domain, we achieved state-of-the-art performance among related recent denoising approaches, both visually and in terms of peak signal-to-noise ratio (PSNR).

Tests of fit for normal inverse Gaussian distributions

2009 ◽  
Vol 6 (6) ◽  
pp. 553-564 ◽  
Author(s):  
K. Fragiadakis ◽  
D. Karlis ◽  
S.G. Meintanis
Keyword(s):  
Inverse Gaussian ◽  
Gaussian Distributions ◽  
Tests Of Fit ◽  
Normal Inverse Gaussian

Multivariate Shrinkage for Image Denoising in Shearlet Domain

2012 ◽  
Vol 239-240 ◽  
pp. 966-969
Author(s):  
Cheng Zhi Deng
Keyword(s):  
Image Denoising ◽  
Signal To Noise Ratio ◽  
Structural Similarity ◽  
Threshold Function ◽  
Maximum A Posteriori ◽  
Inverse Gaussian ◽  
A Posteriori ◽  
Multivariate Normal ◽  
Gaussian Probability Density Function ◽  
Normal Inverse Gaussian

A new multivariate threshold function for image denoising in the shearlet transfrom is proposed. The new threshod exploits a multivariate normal inverse gaussian probability density function to model neighboring shearlet coefficients. Under this prior, a multivariate Bayesian shearlet estimator is derived by using the maximum a posteriori rule. Experimental results show that the new method achieves state-of-art performance in terms of peak signal-to-noise ratio (PSNR), structural similarity (SSIM) index and visual quality than existing shearlet-based image denoising methods.

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