Image Denoising via Bayesian Estimation of Statistical Parameter Using Generalized Gamma Density Prior in Gaussian Noise Model

The need for efficient image denoising methods has grown with the massive production of digital images and movies of all kinds. The distortion of images by additive white Gaussian noise (AWGN) is common during its processing and transmission. This paper is concerned with dual-tree complex wavelet-based image denoising using Bayesian techniques. Indeed, one of the cruxes of the Bayesian image denoising algorithms is to estimate the local variance of the image. Here, we employ maximum a posteriori (MAP) estimation to calculate local observed variance with Maxwell density prior for local observed variance and Gaussian distribution for noisy wavelet coefficients. Evidently, our selection of prior distribution is motivated by analytical and computational tractability. The experimental results show that the proposed method yields good denoising results.

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Image denoising via analytical form of adaptive generalized Gaussian random vectors in AWGN with MMSE estimator for local adaptive parameter

International Journal of Wavelets Multiresolution and Information Processing ◽

10.1142/s0219691315500265 ◽

2015 ◽

Vol 13 (04) ◽

pp. 1550026 ◽

Cited By ~ 2

Author(s):

Pichid Kittisuwan

Keyword(s):

Image Denoising ◽

Additive White Gaussian Noise ◽

Minimum Mean Square Error ◽

Statistical Parameter ◽

Analytical Form ◽

Order Moment ◽

Random Vectors ◽

Adaptive Parameter ◽

Gamma Density ◽

Pearson Type

In this paper, we present new Bayesian estimators for adaptive generalized Gaussian (GG) random vectors in additive white Gaussian noise (AWGN). The derivations are an extension of existing results for Pearson type VII random vectors in AWGN. Pearson type VII random vectors is one of the distribution that successfully use for image denoising. However, Pearson type VII distribution have higher-order moment in statistical parameter for fitted the data such as mean, variance and kurtosis. In our literature, where high-order statistics were used, better performance can be obtained but with much higher computational complexity. In fact, adaptive GG random vectors is similar to Pearson type VII random vectors. However, the special case of adaptive GG random vectors has only first few statistical moments such as adaptive parameter. So, the proposed method can be calculated very fast, without any complex step. In fact, the adaptive parameter of adaptive GG density is the function of standard deviation. Here, we employ minimum mean square error (MMSE) estimation to calculate local observed variances with gamma density prior for local observed variances and Gaussian distribution for noisy wavelet coefficients. In our experiments, our proposed method gives promising denoising results with moderate complexity.

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Image denoising using wavelet transform and wiener filter based on log energy distribution over Poisson-Gaussian noise model

2014 IEEE International Conference on Computational Intelligence and Computing Research ◽

10.1109/iccic.2014.7238350 ◽

2014 ◽

Cited By ~ 2

Author(s):

Ajay Kumar Boyat ◽

Brijendra Kumar Joshi

Keyword(s):

Wavelet Transform ◽

Energy Distribution ◽

Image Denoising ◽

Gaussian Noise ◽

Wiener Filter ◽

Noise Model

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Comparative analysis of different image denoising methods in spatial and transform domain

10.32920/ryerson.14647809 ◽

2021 ◽

Author(s):

Zeeshan Ahmad

Keyword(s):

Comparative Analysis ◽

Image Denoising ◽

Gaussian Noise ◽

Signal To Noise Ratio ◽

Visual Quality ◽

Structural Similarity ◽

Noise Model ◽

Transform Domain ◽

Noise Levels ◽

Extract Information

Digital Images are the best source for humans to see, visualize, think, extract information and make conclusions. However during the acquisition of images, noise superimposes on the images and reduces the information and detail of the images. In order to restore the details of the images, noise must be reduced from the images. This requirement places the image denoising amongst the fundamental and challenging fields of computer vision and image processing. In this project six fundamental techniques / algorithms of image denoising in spatial and transform domain are presented and their comparative analysis is also carried out. The noise model used in this project is Additive Gaussian noise. The algorithms are simulated on Matlab and experimental results are shown at different noise levels. The performance of each image denoising technique is measured in terms of Peak Signal to Noise Ratio (PSNR) , Mean Structural Similarity (SSIM) Metrics and visual quality. It is observed that the transform domain techniques used in this project achieved better results as compared to spatial domain techniques

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POSITIVELY CONSTRAINED TOTAL VARIATION PENALIZED IMAGE RESTORATION

Advances in Adaptive Data Analysis ◽

10.1142/s1793536911000817 ◽

2011 ◽

Vol 03 (01n02) ◽

pp. 187-201 ◽

Cited By ~ 6

Author(s):

RAYMOND H. CHAN ◽

HAI-XIA LIANG ◽

JUN MA

Keyword(s):

Image Processing ◽

Image Restoration ◽

Total Variation ◽

Gaussian Noise ◽

Impulsive Noise ◽

Noise Model ◽

Splitting Algorithm ◽

New Approach ◽

Tomographic Image Reconstruction ◽

Noise Models

The total variation (TV) minimization models are widely used in image processing, mainly due to their remarkable ability in preserving edges. There are many methods for solving the TV model. These methods, however, seldom consider the positivity constraint one should impose on image-processing problems. In this paper we develop and implement a new approach for TV image restoration. Our method is based on the multiplicative iterative algorithm originally developed for tomographic image reconstruction. The advantages of our algorithm are that it is very easy to derive and implement under different image noise models and it respects the positivity constraint. Our method can be applied to various noise models commonly used in image restoration, such as the Gaussian noise model, the Poisson noise model, and the impulsive noise model. In the numerical tests, we apply our algorithm to deblur images corrupted by Gaussian noise. The results show that our method give better restored images than the forward–backward splitting algorithm.

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Comparative analysis of different image denoising methods in spatial and transform domain

10.32920/ryerson.14647809.v1 ◽

2021 ◽

Author(s):

Zeeshan Ahmad

Keyword(s):

Comparative Analysis ◽

Image Denoising ◽

Gaussian Noise ◽

Signal To Noise Ratio ◽

Visual Quality ◽

Structural Similarity ◽

Noise Model ◽

Transform Domain ◽

Noise Levels ◽

Extract Information

Digital Images are the best source for humans to see, visualize, think, extract information and make conclusions. However during the acquisition of images, noise superimposes on the images and reduces the information and detail of the images. In order to restore the details of the images, noise must be reduced from the images. This requirement places the image denoising amongst the fundamental and challenging fields of computer vision and image processing. In this project six fundamental techniques / algorithms of image denoising in spatial and transform domain are presented and their comparative analysis is also carried out. The noise model used in this project is Additive Gaussian noise. The algorithms are simulated on Matlab and experimental results are shown at different noise levels. The performance of each image denoising technique is measured in terms of Peak Signal to Noise Ratio (PSNR) , Mean Structural Similarity (SSIM) Metrics and visual quality. It is observed that the transform domain techniques used in this project achieved better results as compared to spatial domain techniques

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Variable Splitting Based Method for Image Restoration with Impulse Plus Gaussian Noise

Mathematical Problems in Engineering ◽

10.1155/2016/3151303 ◽

2016 ◽

Vol 2016 ◽

pp. 1-16 ◽

Cited By ~ 2

Author(s):

Tingting Wu

Keyword(s):

Image Processing ◽

Image Denoising ◽

Gaussian Noise ◽

Fundamental Problem ◽

Noise Removal ◽

Phase Method ◽

Two Phase ◽

Variable Splitting ◽

Mixed Noise ◽

Mixed Noise Removal

Image denoising is a fundamental problem in realm of image processing. A large amount of literature is dedicated to restoring an image corrupted by a certain type of noise. However, little literature is concentrated on the scenario of mixed noise removal. In this paper, based on the model of two-phase method for image denoising proposed by Cai et al. (2008) and the idea of variable splitting, we are capable of decomposing the image denoising problem into subproblems with closed form. Numerical results illustrate the validity and robustness of the proposed algorithms, especially for restoring the images contaminated by impulse plus Gaussian noise.

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