An Efficient, Closed-Form MAP Estimator for Nakagami- ${m}$ Fading Parameter

2016 ◽  
Vol 20 (11) ◽  
pp. 2328-2331 ◽  
Author(s):  
Pedro Luiz Ramos ◽  
Francisco Louzada ◽  
Eduardo Ramos
Keyword(s):  
Closed Form ◽  
Map Estimator ◽  
Fading Parameter

Despeckling method of ultrasound images using closed-form shrinkage function based on cauchy distribution in wavelet domain

2020 ◽  
Vol 18 (04) ◽  
pp. 2050026
Author(s):  
Kyong-Il Kim ◽  
Soon-Ic Bahng ◽  
Ryong-Nam Choe
Keyword(s):  
Closed Form ◽  
Image Denoising ◽  
Ultrasound Image ◽  
Speckle Noise ◽  
The Other ◽  
Ultrasound Images ◽  
Wavelet Domain ◽  
Wavelet Coefficients ◽  
Shrinkage Function ◽  
Map Estimator

Speckle suppression and elimination are very important to improve the visual quality of ultrasound image and the diagnostic ability of the diseases. An effective technique of image denoising based on discrete wavelet transform is to employ a Bayesian maximum a posteriori (MAP) estimator. To suppress and remove the speckle noise using MAP estimator effectively, it must assign correctly the shrinkage function based on appropriate probability density functions (PDFs) for the wavelet coefficients of logarithmically transformed noise-free ultrasound image and speckle noise. In this paper, we introduce a new closed-form shrinkage function that is an analytical solution of a Bayesian MAP estimator for despeckling of the ultrasound images effectively in wavelet domain. We employ a Cauchy prior and Gaussian PDF to model the wavelet coefficients of logarithmically transformed noise-free ultrasound image and speckle noise, respectively. Firstly, we derive the CauchyShrinkGMAP that is a closed-form shrinkage function. In addition, we estimate the noise variance and parameter of MAP estimator. Next, we evaluate the despeckling performance of wavelet image denoising method using the CauchyShrinkGMAP compared to various despeckling method using median and Wiener filters, hard and soft thresholding and GaussShrinkGMAP and MCMAP3N shrinkage function. The experiment results show that PSNR of new closed-form shrinkage function is highest, MSE is smallest, and the correlation coefficient ([Formula: see text]) and SSIM are closer to one than the other existing image denoising methods for noisy synthetic ultrasound images at different speckle noise levels. Also, experiment results show that ENL of new closed-form shrinkage function is highest and that of EN and SD is smallest than the other existing image denoising methods for noisy real ultrasound image.

scholarly journals Performance Analysis and Optimization of RIS-Assisted Networks in Nakagami-m Environment

2021 ◽  
Author(s):  
Monjed H. Samuh ◽  
Ahmed H. Abd El-Malek ◽  
Keyword(s):  
Outage Probability ◽  
Closed Form ◽  
Signal To Noise Ratio ◽  
Closed Form Expression ◽  
High Signal ◽  
Optimum Number ◽  
Diversity Order ◽  
Symbol Error Probability ◽  
Fading Parameter ◽  
Performance Results

Abstract This work studies and optimizes the performance of reconfigurable intelligent surface (RIS)-aided networks in Nakagami- m fading environment. First, accurate closed-form approximations for the channel distributions are derived. Then, closed-form formulas for the system outage probability, average symbol error probability (ASEP), and the channel capacity are obtained. Furthermore, we provide three different optimization approaches for finding the optimum number of reflecting elements to achieve a target outage probability. At the high signal-to-noise ratio (SNR) regime, a closed-form expression for the asymptotic outage probability is obtained to give more insights into the system performance. Results show that the considered system can achieve a diversity order of, where a is a function of the Nakagami- m fading parameter m and the number of reflecting elements N . Moreover, findings show that m is more influential on the diversity order than N . Finally, the achieved expressions are applicable to non-integer values of m and any number of meta-surface elements N .

Closed Form Solutions of Joint Water-Filling for Coordinated Transmission

2010 ◽  
Vol E93-B (12) ◽  
pp. 3461-3468 ◽  
Author(s):  
Bing LUO ◽  
Qimei CUI ◽  
Hui WANG ◽  
Xiaofeng TAO ◽  
Ping ZHANG
Keyword(s):  
Closed Form ◽  
Closed Form Solutions ◽  
Water Filling
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