Variational approach for edge-preserving regularization using coupled PDEs
- 1 March 1998
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Image Processing
- Vol. 7 (3) , 387-397
- https://doi.org/10.1109/83.661189
Abstract
This paper deals with edge-preserving regularization for inverse problems in image processing. We first present a synthesis of the main results we have obtained in edge-preserving regularization by using a variational approach. We recall the model involving regularizing functions phi and we analyze the geometry-driven diffusion process of this model in the three-dimensional (3-D) case. Then a half-quadratic theorem is used to give a very simple reconstruction algorithm. After a critical analysis of this model, we propose another functional to minimize for edge-preserving reconstruction purposes. It results in solving two coupled partial differential equations (PDEs): one processes the intensity, the other the edges. We study the relationship with similar PDE systems in particular with the functional proposed by Ambrosio-Tortorelli in order to approach the Mumford-Shah functional developed in the segmentation application. Experimental results on synthetic and real images are presented.Keywords
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