Adaptive Coupled PDE System for Image Restoration
We consider a coupled system of partial differential equations (PDEs) based model for image restoration. Both the image and the edge variables are incorporated by coupling them into two different PDEs. It is shown that the initial-boundary value problem has global in time dissipative solutions (in a sense going back to P.-L. Lions), and several properties of these solutions are established. Some numerical examples are given to highlight the denoising nature of the proposed model along with some comparison results.
Comparison with Classical Schemes
Perona and Malik 
Catte et al 
ADAP Coupled PDE 
Comparison with Other PDE Schemes
Method Noise |u0-u|
Example Medical Image Denoising Result
Edge Variable v
Lets look at the Brain image denoising in a better way
Noisy input image
Smoothed output image
Residue (w = u0-(u+v))
If you use the images presented here kindly cite Reference  below.
 V. B. S. prasath, D. Vorotnikov. On a system of adaptive coupled PDEs for image restoration. Journal of Mathematical Imaging and Vision, 48(1):35-52, 2014. doi:10.1007/s10851-012-0386-3. Preliminary version at arXiv, December 2011. doi:10.48550/arXiv.1112.2904.
Related Talk: Global dissipative solutions for generalized forward-backward diffusion equations, at The Third Ohio River Analysis Meeting, March 8-10, 2013, University of Cincinnati, OH, USA. Slides available at figshare: 10.6084/m9.figshare.646651.
$The first author (VBSP) thanks the Fields Institute, Toronto, Canada for their great hospitality and support during the Thematic Program on Inverse Problems and Imaging where part of this work was done. The second author (DV) was partially supported by CMUC and FCT (Portugal), through European Program COMPETE/FEDER.
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