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A modified multi-grid algorithm for a novel variational model to remove multiplicative noise
- Source :
- Journal of Visual Communication and Image Representation. 40:485-501
- Publication Year :
- 2016
- Publisher :
- Elsevier BV, 2016.
-
Abstract
- This paper proposes a novel variational model and a fast algorithm for its numerical approximation to remove multiplicative noise from digital images.By applying a maximum a posteriori (MAP), we obtained a strictly convex objective functional whose minimization leads to non-linear PDEs.To this end, we develop an efficient non-linear multi-grid algorithm with an improved smoother and also discuss a local Fourier analysis of the associated smoothers which leads to a new and more effective smoother.Experimental results using both synthetic and realistic images, illustrate advantages of our proposed model in visual improvement as well as an increase in the PSNR over comparing to related recent corresponding PDE methods.We compare numerical results of new multi-grid algorithm via modified smoother with traditional time marching schemes and with multi-grid method via (local and global) fixed point smoother as well. This paper proposes a novel variational model and a fast algorithm for its numerical approximation to remove multiplicative noise from digital images. By applying a maximum a posteriori (MAP), we obtained a strictly convex objective functional whose minimization leads to non-linear partial differential equations. As a result, developing a fast numerical scheme is difficult because of the high nonlinearity and stiffness of the associated Euler-Lagrange equation and standard unilevel iterative methods are not appropriate. To this end, we develop an efficient non-linear multi-grid algorithm with an improved smoother. We also discuss a local Fourier analysis of the associated smoothers which leads to a new and more effective smoother. Experimental results using both synthetic and realistic images, illustrate advantages of our proposed model in visual improvement as well as an increase in the peak signal-to-noise ratio over comparing to related recent corresponding PDE methods. We compare numerical results of new multigrid algorithm via modified smoother with traditional time marching schemes and with multigrid method via (local and global) fixed point smoother as well.
- Subjects :
- Partial differential equation
Iterative method
ComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISION
MathematicsofComputing_NUMERICALANALYSIS
010103 numerical & computational mathematics
02 engineering and technology
Fixed point
01 natural sciences
Multiplicative noise
Nonlinear system
Multigrid method
Signal Processing
0202 electrical engineering, electronic engineering, information engineering
Media Technology
Maximum a posteriori estimation
020201 artificial intelligence & image processing
Computer Vision and Pattern Recognition
0101 mathematics
Electrical and Electronic Engineering
Convex function
Algorithm
Mathematics
Subjects
Details
- ISSN :
- 10473203
- Volume :
- 40
- Database :
- OpenAIRE
- Journal :
- Journal of Visual Communication and Image Representation
- Accession number :
- edsair.doi...........876c30297e40ed1481ae043656e2edb4