scholarly journals On removing blur in images using least squares solutions

Filomat ◽  
2016 ◽  
Vol 30 (14) ◽  
pp. 3855-3866
Author(s):  
Predrag Stanimirovic ◽  
Igor Stojanovic ◽  
Dimitrios Pappas ◽  
Spiros Chountasis ◽  
Zoran Zdravev
Keyword(s):  
Statistical Analysis ◽  
Image Restoration ◽  
Least Squares ◽  
Numerical Results ◽  
Tikhonov Regularization Method ◽  
Truncated Singular Value Decomposition ◽  
Singular Value Decomposition Method ◽  
Restoration Method ◽  
Value Decomposition ◽  
Least Squares Approach

The further investigation of the image restoration method introduced in [19, 20] is presented in this paper. Continuing investigations in that area, two additional applications of the method are investigated. More precisely, we consider the possibility to replace the available matrix in the method by the restoration obtained applying the Tikhonov regularization method or the Truncated Singular Value decomposition method. Additionally, statistical analysis of numerical results generated by applying the proposed improvement of image restoration methods is presented. Previously performed numerical experiments as well as new numerical results and the statistical analysis confirm that the least squares approach can be used as a useful tool for improving restored images obtained by other image restoration methods.

scholarly journals A modified truncation singular value decomposition method for solving ill-posed problems

2018 ◽  
Vol 13 ◽  
pp. 174830181881360 ◽  
Author(s):  
Zhenyu Zhao ◽  
Riguang Lin ◽  
Zehong Meng ◽  
Guoqiang He ◽  
Lei You ◽  
...  
Keyword(s):  
Singular Value Decomposition ◽  
Decomposition Method ◽  
Singular Value ◽  
Numerical Results ◽  
New Method ◽  
Truncated Singular Value Decomposition ◽  
Singular Value Decomposition Method ◽  
Ill Posed ◽  
Value Decomposition

A modified truncated singular value decomposition method for solving ill-posed problems is presented in this paper, in which the solution has a slightly different form. Both theoretical and numerical results show that the limitations of the classical TSVD method have been overcome by the new method and very few additive computations are needed.

scholarly journals Heterogeneous Correlation Map Between Estimated ENSO And IOD From ERA5 And Hotspot In Indonesia

2021 ◽  
Vol 3 (2) ◽  
pp. 65-72
Author(s):  
Sri Nurdiati ◽  
Fahren Bukhari ◽  
Muhammad Tito Julianto ◽  
Mohamad Khoirun Najib ◽  
Nuzhatun Nazria
Keyword(s):  
Statistical Analysis ◽  
Decomposition Method ◽  
Southern Oscillation ◽  
Weather Forecast ◽  
Singular Value ◽  
Singular Value Decomposition Method ◽  
Substantial Correlation ◽  
Correlation Strength ◽  
Value Decomposition ◽  
Variance Explained

El Nino-Southern Oscillation (ENSO) and Indian Ocean Dipole (IOD) can reduce the amount of rainfall in Indonesia. The previous study found that ENSO and IOD derived from the OISST dataset have an association with hotspots in Indonesia, especially in southern Sumatra dan Kalimantan. But the correlation results are still too small, and the correlation strength between regions has not been analyzed. Therefore, this study quantifies the association of the estimated ENSO and IOD derived from the ERA5 dataset on hotspots in Indonesia based on a Heterogeneous Correlation Map (HCM) and analyzes the correlation strength between regions in Indonesia. We use a singular value decomposition method to quantify this HCM. Besides OISST, ERA5 is an estimation data often used for weather forecast analysis. Therefore, this study quantifies the association of the estimated ENSO and IOD derived from the ERA5 dataset on hotspots in Indonesia based on a Heterogeneous Correlation Map (HCM) and analyzes the correlation strength between regions in Indonesia. Based on variance explained and correlation strength, the hotspot in Indonesia is more sensitive to ENSO and IOD derived from ERA5 than OISST. Consequently, the ERA5 data more useful to statistical analysis that requiring a substantial correlation.

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