Image denoising via Bayesian estimation of local variance with Maxwell density prior

2015 ◽  
Vol 06 (02) ◽  
pp. 1550002
Author(s):  
Pichid Kittisuwan
Keyword(s):  
Image Denoising ◽  
Gaussian Noise ◽  
Prior Distribution ◽  
Additive White Gaussian Noise ◽  
Maximum A Posteriori ◽  
Map Estimation ◽  
A Posteriori ◽  
Bayesian Techniques ◽  
Local Variance ◽  
Selection Of

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.

scholarly journals Threshold Computation for Spatially Coupled Turbo-Like Codes on the AWGN Channel

Entropy ◽  
2021 ◽  
Vol 23 (2) ◽  
pp. 240
Author(s):  
Muhammad Umar Farooq ◽  
Alexandre Graell i Amat ◽  
Michael Lentmaier
Keyword(s):  
Gaussian Noise ◽  
Belief Propagation ◽  
Additive White Gaussian Noise ◽  
Maximum A Posteriori ◽  
Prediction Methods ◽  
Threshold Analysis ◽  
A Posteriori ◽  
Awgn Channel ◽  
Efficient Prediction ◽  
Binary Erasure Channel

In this paper, we perform a belief propagation (BP) decoding threshold analysis of spatially coupled (SC) turbo-like codes (TCs) (SC-TCs) on the additive white Gaussian noise (AWGN) channel. We review Monte-Carlo density evolution (MC-DE) and efficient prediction methods, which determine the BP thresholds of SC-TCs over the AWGN channel. We demonstrate that instead of performing time-consuming MC-DE computations, the BP threshold of SC-TCs over the AWGN channel can be predicted very efficiently from their binary erasure channel (BEC) thresholds. From threshold results, we conjecture that the similarity of MC-DE and predicted thresholds is related to the threshold saturation capability as well as capacity-approaching maximum a posteriori (MAP) performance of an SC-TC ensemble.

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

2015 ◽  
Vol 14 (02) ◽  
pp. 1550017
Author(s):  
Pichid Kittisuwan
Keyword(s):  
Image Processing ◽  
Image Denoising ◽  
Gaussian Noise ◽  
Classical Problem ◽  
Statistical Parameter ◽  
Noise Model ◽  
Natural Image ◽  
Bayesian Techniques ◽  
Generalized Gamma ◽  
Gamma Density

The application of image processing in industry has shown remarkable success over the last decade, for example, in security and telecommunication systems. The denoising of natural image corrupted by Gaussian noise is a classical problem in image processing. So, image denoising is an indispensable step during image processing. This paper is concerned with dual-tree complex wavelet-based image denoising using Bayesian techniques. One of the cruxes of the Bayesian image denoising algorithms is to estimate the statistical parameter of the image. Here, we employ maximum a posteriori (MAP) estimation to calculate local observed variance with generalized Gamma density prior for local observed variance and Laplacian or Gaussian distribution for noisy wavelet coefficients. Evidently, our selection of prior distribution is motivated by efficient and flexible properties of generalized Gamma density. The experimental results show that the proposed method yields good denoising results.

scholarly journals Continuous Finger Gesture Recognition Based on Flex Sensors

Sensors ◽  
2019 ◽  
Vol 19 (18) ◽  
pp. 3986 ◽  
Author(s):  
Wei-Chieh Chuang ◽  
Wen-Jyi Hwang ◽  
Tsung-Ming Tai ◽  
De-Rong Huang ◽  
Yun-Jie Jhang
Keyword(s):  
Gesture Recognition ◽  
Recognition System ◽  
Maximum A Posteriori ◽  
Map Estimation ◽  
A Posteriori ◽  
Sensory Data ◽  
Robust Recognition ◽  
Flex Sensors ◽  
Gated Recurrent Unit ◽  
Gesture Spotting

The goal of this work is to present a novel continuous finger gesture recognition system based on flex sensors. The system is able to carry out accurate recognition of a sequence of gestures. Wireless smart gloves equipped with flex sensors were implemented for the collection of the training and testing sets. Given the sensory data acquired from the smart gloves, the gated recurrent unit (GRU) algorithm was then adopted for gesture spotting. During the training process for the GRU, the movements associated with different fingers and the transitions between two successive gestures were taken into consideration. On the basis of the gesture spotting results, the maximum a posteriori (MAP) estimation was carried out for the final gesture classification. Because of the effectiveness of the proposed spotting scheme, accurate gesture recognition was achieved even for complicated transitions between successive gestures. From the experimental results, it can be observed that the proposed system is an effective alternative for robust recognition of a sequence of finger gestures.

scholarly journals New approach to Bayesian high-dimensional linear regression

2018 ◽  
Vol 7 (4) ◽  
pp. 605-655 ◽  
Author(s):  
Shirin Jalali ◽  
Arian Maleki
Keyword(s):  
Linear Regression ◽  
Sampling Rate ◽  
High Dimensional ◽  
Maximum A Posteriori ◽  
Map Estimation ◽  
A Posteriori ◽  
Fundamental Limits ◽  
New Approach ◽  
Estimation Scheme ◽  
Response Variables

Abstract Consider the problem of estimating parameters $X^n \in \mathbb{R}^n $, from $m$ response variables $Y^m = AX^n+Z^m$, under the assumption that the distribution of $X^n$ is known. Lack of computationally feasible algorithms that employ generic prior distributions and provide a good estimate of $X^n$ has limited the set of distributions researchers use to model the data. To address this challenge, in this article, a new estimation scheme named quantized maximum a posteriori (Q-MAP) is proposed. The new method has the following properties: (i) In the noiseless setting, it has similarities to maximum a posteriori (MAP) estimation. (ii) In the noiseless setting, when $X_1,\ldots,X_n$ are independent and identically distributed, asymptotically, as $n$ grows to infinity, its required sampling rate ($m/n$) for an almost zero-distortion recovery approaches the fundamental limits. (iii) It scales favorably with the dimensions of the problem and therefore is applicable to high-dimensional setups. (iv) The solution of the Q-MAP optimization can be found via a proposed iterative algorithm that is provably robust to error (noise) in response variables.

A Non-Local Image Denoising Technique Using Adaptive Filter Parameter

2014 ◽  
Vol 556-562 ◽  
pp. 4839-4842
Author(s):  
Song Yuan Tang
Keyword(s):  
Image Denoising ◽  
Gaussian Noise ◽  
Additive White Gaussian Noise ◽  
Wiener Filter ◽  
White Gaussian Noise ◽  
Filter Parameter ◽  
Iterative Computation ◽  
Local Mean ◽  
Non Local

This paper proposes a method to obtain the optimal filter parameter of the non-local mean (NLM) algorithm. The parameter is assumed to be a function of the variance of the additive white Gaussian noise and is adaptive estimated. The initialization of the variance of the additive white Gaussian noise is estimated by Wiener filter. Then the NLM filter is used to adaptively estimate the noise variance. The image denoising is an iterative computation till the parameter convergence. Experiments show that the proposed method can improve the quality of the denoised images efficiently.

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