joint with Jinjun Xu, Wotao Yin and Donald Goldfarb
Total Variation based regularization and image restoration was developed by Rudin-Osher-Fatemi in the late 80's. Recently, Yves Meyer characterized textures as elements of the dual of BV and did some extremely interesting analysis on the original ROF model. This led to practical algorithms to decompose images into structure plus texture.
Very promising results involving processing image gradients simultaneously with images were obtained by Lysaker-Osher-Tai, based on earlier work on processing surfaces by Tasdizen-Whitaker-Burchard-Osher. This has now led to a new way of refining and enhancing the solutions to a wide class of inverse problems. I will discuss all this and present image restoration results which appear to be state-of-the-art.
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