Lower bound on average mean-square error for image restoration

1991 ◽  
Vol 39 (2) ◽  
pp. 497-499 ◽  
Author(s):  
H. Hung
Keyword(s):  
Lower Bound ◽  
Image Restoration ◽  
Mean Square Error ◽  
Mean Square ◽  
Average Mean Square Error

Detection of Biomedical Images by Using Bio-inspired Artificial Intelligent

2020 ◽  
Vol 38 (2A) ◽  
pp. 255-264
Author(s):  
Hanan A. R. Akkar ◽  
Sameem A. Salman
Keyword(s):  
Neural Network ◽  
Artificial Neural Network ◽  
Mean Square Error ◽  
Average Rate ◽  
Mean Square ◽  
Performance Measurements ◽  
Artificial Intelligent ◽  
Average Mean Square Error ◽  
Artificial Neural ◽  
Artificial Neural Network Ann

Computer vision and image processing are extremely necessary for medical pictures analysis. During this paper, a method of Bio-inspired Artificial Intelligent (AI) optimization supported by an artificial neural network (ANN) has been widely used to detect pictures of skin carcinoma. A Moth Flame Optimization (MFO) is utilized to educate the artificial neural network (ANN). A different feature is an extract to train the classifier. The comparison has been formed with the projected sample and two Artificial Intelligent optimizations, primarily based on classifier especially with, ANN-ACO (ANN training with Ant Colony Optimization (ACO)) and ANN-PSO (training ANN with Particle Swarm Optimization (PSO)). The results were assessed using a variety of overall performance measurements to measure indicators such as Average Rate of Detection (ARD), Average Mean Square error (AMSTR) obtained from training, Average Mean Square error (AMSTE) obtained for testing the trained network, the Average Effective Processing Time (AEPT) in seconds, and the Average Effective Iteration Number (AEIN). Experimental results clearly show the superiority of the proposed (ANN-MFO) model with different features.

scholarly journals Optical Determination In The Positions Of Radio Stars

1988 ◽  
Vol 133 ◽  
pp. 497-500
Author(s):  
Xu Tong-qi ◽  
Lu Pei-zhen ◽  
Chu Zong-yuan ◽  
Wang Shu-he
Keyword(s):  
Mean Square Error ◽  
Mean Square ◽  
Single Observation ◽  
Average Mean Square Error ◽  
Optical Determination ◽  
The Right ◽  
Magnitude Difference ◽  
Right Ascension ◽  
Radio Stars

Optical positions of 16 radio stars have been derived from 40 cm astrograph at Zô-Sè. The reference catalogues are AGK3 and SAO, the average mean square error of single observation is 0″.058 in the right ascension and 0″.053 in declination. The magnitude difference has no significant effect on the observations.

The Cramer–Rao lower bound in a non-AWGN model for the affine phase retrieval

2021 ◽  
pp. 2050089
Author(s):  
Zhitao Zhuang ◽  
Kaixin Wang
Keyword(s):  
Lower Bound ◽  
Mean Square Error ◽  
Gaussian Noise ◽  
Phase Retrieval ◽  
Additive White Gaussian Noise ◽  
White Gaussian Noise ◽  
Mean Square ◽  
Cramer Rao Lower Bound ◽  
The Difference

In this paper, we derive the Cramer–Rao lower bound (CRLB) in a non-additive white Gaussian noise (AWGN) model for the affine phase retrieval (APR) and simulate the difference of CRLB and mean square error produced by PhaseLift of phase retrieval and APR in AWGN and non-AWGN cases.

scholarly journals Comparing Parameter Estimation of Random Coefficient Autoregressive Model by Frequentist Method

Mathematics ◽  
2020 ◽  
Vol 8 (1) ◽  
pp. 62 ◽  
Author(s):  
Autcha Araveeporn
Keyword(s):  
Maximum Likelihood ◽  
Least Squares ◽  
Mean Square Error ◽  
Maximum Likelihood Method ◽  
Least Squares Method ◽  
Likelihood Function ◽  
Likelihood Method ◽  
Mean Square ◽  
Average Mean Square Error ◽  
Frequentist Method

This paper compares the frequentist method that consisted of the least-squares method and the maximum likelihood method for estimating an unknown parameter on the Random Coefficient Autoregressive (RCA) model. The frequentist methods depend on the likelihood function that draws a conclusion from observed data by emphasizing the frequency or proportion of the data namely least squares and maximum likelihood methods. The method of least squares is often used to estimate the parameter of the frequentist method. The minimum of the sum of squared residuals is found by setting the gradient to zero. The maximum likelihood method carries out the observed data to estimate the parameter of a probability distribution by maximizing a likelihood function under the statistical model, while this estimator is obtained by a differential parameter of the likelihood function. The efficiency of two methods is considered by average mean square error for simulation data, and mean square error for actual data. For simulation data, the data are generated at only the first-order models of the RCA model. The results have shown that the least-squares method performs better than the maximum likelihood. The average mean square error of the least-squares method shows the minimum values in all cases that indicated their performance. Finally, these methods are applied to the actual data. The series of monthly averages of the Stock Exchange of Thailand (SET) index and daily volume of the exchange rate of Baht/Dollar are considered to estimate and forecast based on the RCA model. The result shows that the least-squares method outperforms the maximum likelihood method.

scholarly journals Performance Analysis of ANN Model for Estimation of Trophic Status Index of Lakes

2018 ◽  
Vol 7 (1) ◽  
pp. 1
Author(s):  
Tushar Anthwal ◽  
Akanksha Chandola ◽  
M P Thapliyal
Keyword(s):  
Mean Square Error ◽  
Trophic Status ◽  
Error Function ◽  
Water Bodies ◽  
Mean Square ◽  
Ann Model ◽  
Feed Forward Back Propagation ◽  
Average Mean Square Error ◽  
Quasi Newton ◽  
Status Index

The health of water bodies across the globe is of high concern as the pollution is accelerating rigorously. With the interventions of simple technology, some significant changes could be bought up. Lakes are dying because of high Trophic Index Status which shows the eutrophication level of water bodies. Taking this into account, feed forward back propagation neural network model is used to estimate the Trophic Status Index (TSI) of lakes which could compute the value of TSI with the given parameters; pH, temperature, dissolved oxygen, Secchi disk transparency, chlorophyll and total phosphate. Two learning algorithms; Levenberg Marquardt (LM) and Broyden–Fletcher–Goldfarb–Shanno (BFGS) Quasi Newton were used to train the network, which belongs to different classes. The results were analyzed using mean square error function and further checked for the deviation from actual data. Among both the training algorithm; LM demonstrated better performance with 0.0007 average mean square error for best validation performance and BFGS Quasi Newton shows the average mean square error of 1.07.

scholarly journals Self-Similarity Sparse Representation for Image Restoration

2019 ◽  
Vol 8 (2S11) ◽  
pp. 1063-1067
Keyword(s):  
Image Restoration ◽  
Mean Square Error ◽  
Gaussian Noise ◽  
Local Similarity ◽  
Mean Square ◽  
Regularization Term ◽  
Local Regularization ◽  
Degraded Image ◽  
Local Patterns ◽  
Non Local

Image restoration aims to restore an image from a degraded image. The degradation may occur during image acquisition or image transmission. Image degradation lowers the quality of the image. In this paper additive Gaussian noise is considered for degrading the original image. For restoring the image from degraded image the proposed method used both local and non-local similarity patterns. The restoration problem is modeled with regression model. Two regularization terms are considered for representing prior image information. One regularization term is for local patterns and other is for non-local similarity patterns. The additive local regularization term is used to restore the edges. The non-local regularization term works best for local smoothness and edge information will be lost. The proposed algorithm took a clean image of size 256x256 and added with Gaussian noise with different levels of noise levels. A self-adaptive dictionary is trained for a particular window of image with local and non-local patterns and stacked to three dimensional matrix. The patch size considered for training the dictionary is 10x10. For restoring each patch it searches best atoms form the trained dictionary. The efficiency of the algorithm is estimated by parameters mean square error, root mean square error, PSNR and FSIM. The algorithm is also tested for different images like cameraman, house, Barbara, Lena and parrot. The proposed algorithm is tested with conventional algorithms. .

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