A modified fixed-point iterative algorithm for image restoration using fourth-order PDE model

2012 ◽  
Vol 62 (2) ◽  
pp. 79-90 ◽  
Author(s):  
Ting-Ting Wu ◽  
Yu-Fei Yang ◽  
Zhi-Feng Pang
Keyword(s):  
Fixed Point ◽  
Image Restoration ◽  
Iterative Algorithm ◽  
Fourth Order ◽  
Pde Model ◽  
Fourth Order Pde

scholarly journals A Multiplicative Noise Removal Approach Based on Partial Differential Equation Model

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Bo Chen ◽  
Jin-Lin Cai ◽  
Wen-Sheng Chen ◽  
Yan Li
Keyword(s):  
Fourth Order ◽  
Multiplicative Noise ◽  
Additive Noise ◽  
Speckle Noise ◽  
Noise Removal ◽  
Equation Model ◽  
Superior Performance ◽  
Pde Model ◽  
Novel Approach ◽  
Fourth Order Pde

Multiplicative noise, also known as speckle noise, is signal dependent and difficult to remove. Based on a fourth-order PDE model, this paper proposes a novel approach to remove the multiplicative noise on images. In practice, Fourier transform and logarithm strategy are utilized on the noisy image to convert the convolutional noise into additive noise, so that the noise can be removed by using the traditional additive noise removal algorithm in frequency domain. For noise removal, a new fourth-order PDE model is developed, which avoids the blocky effects produced by second-order PDE model and attains better edge-preserve ability. The performance of the proposed method has been evaluated on the images with both additive and multiplicative noise. Compared with some traditional methods, experimental results show that the proposed method obtains superior performance on different PSNR values and visual quality.

Some fixed point results for (β-ψ1-ψ2)-contractive conditions in ordered b-metric-like spaces

Filomat ◽  
2017 ◽  
Vol 31 (14) ◽  
pp. 4587-4612 ◽  
Author(s):  
S.K. Padhan ◽  
Rao Jagannadha ◽  
Hemant Nashine ◽  
R.P. Agarwal
Keyword(s):  
Fixed Point ◽  
Boundary Value Problems ◽  
Fourth Order ◽  
Metric Spaces ◽  
Contractive Mapping ◽  
Existence Of Solution ◽  
Distance Functions ◽  
Point Boundary ◽  
Contractive Mappings ◽  
Altering Distance

This paper extends and generalizes results of Mukheimer [(?,?,?)-contractive mappings in ordered partial b-metric spaces, J. Nonlinear Sci. Appl. 7(2014), 168-179]. A new concept of (?-?1-?2)-contractive mapping using two altering distance functions in ordered b-metric-like space is introduced and basic fixed point results have been studied. Useful examples are illustrated to justify the applicability and effectiveness of the results presented herein. As an application, the existence of solution of fourth-order two-point boundary value problems is discussed and rationalized by a numerical example.

scholarly journals A Cyclic Iterative Algorithm for Multiple-Sets Split Common Fixed Point Problem of Demicontractive Mappings without Prior Knowledge of Operator Norm

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 372
Author(s):  
Nishu Gupta ◽  
Mihai Postolache ◽  
Ashish Nandal ◽  
Renu Chugh
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Prior Knowledge ◽  
Iterative Algorithm ◽  
Fixed Point Problem ◽  
Null Point ◽  
Operator Norm ◽  
Point Problem ◽  
Common Fixed Point Problem ◽  
Split Common Fixed Point

The aim of this paper is to formulate and analyze a cyclic iterative algorithm in real Hilbert spaces which converges strongly to a common solution of fixed point problem and multiple-sets split common fixed point problem involving demicontractive operators without prior knowledge of operator norm. Significance and range of applicability of our algorithm has been shown by solving the problem of multiple-sets split common null point, multiple-sets split feasibility, multiple-sets split variational inequality, multiple-sets split equilibrium and multiple-sets split monotone variational inclusion.

scholarly journals The Improvement of ROF De-noising Model Based on AOS and Fourth-order PDE

2011 ◽  
Vol 15 ◽  
pp. 2778-2782 ◽  
Author(s):  
Yonghong Zhang ◽  
Yang Ding ◽  
Lihua Wang
Keyword(s):  
Fourth Order ◽  
Model Based ◽  
Fourth Order Pde
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