fourth order pde
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Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 930
Author(s):  
Tudor Barbu

A digital image compression framework based on nonlinear partial differential equations (PDEs) is proposed in this research article. First, a feature keypoint-based sparsification algorithm is proposed for the image coding stage. The interest keypoints corresponding to various scale-invariant image feature descriptors, such as SIFT, SURF, MSER, ORB, and BRIEF, are extracted, and the points from their neighborhoods are then used as sparse pixels and coded using a lossless encoding scheme. An effective nonlinear fourth-order PDE-based scattered data interpolation is proposed for solving the decompression task. A rigorous mathematical investigation of the considered PDE model is also performed, with the well-posedness of this model being demonstrated. It is then solved numerically by applying a consistent finite difference method-based numerical approximation algorithm that is next successfully applied in the image compression and decompression experiments, which are also discussed in this work.


2020 ◽  
Vol 25 (1) ◽  
pp. 415-442
Author(s):  
Amine Laghrib ◽  
◽  
Abdelkrim Chakib ◽  
Aissam Hadri ◽  
Abdelilah Hakim ◽  
...  

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