Directional Framelets with Low Redundancy and Directional Quasi-tight Framelets
Duration: 40 mins 4 secs
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| Description: |
Han, B
Tuesday 19th February 2019 - 11:40 to 12:15 |
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| Created: | 2019-02-20 12:59 |
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| Collection: | Approximation, sampling and compression in data science |
| Publisher: | Isaac Newton Institute |
| Copyright: | Han, B |
| Language: | eng (English) |
| Distribution: |
World
(downloadable)
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| Explicit content: | No |
| Aspect Ratio: | 16:9 |
| Screencast: | No |
| Bumper: | UCS Default |
| Trailer: | UCS Default |
| Abstract: | Edge singularities are ubiquitous and hold key information for many high-dimensional problems. Consequently, directional representation systems are required to effectively capture edge singularities for high-dimensional problems. However, the increased angular resolution often significantly increases the redundancy rates of a directional system. High redundancy rates lead to expensive computational costs and large storage requirement, which hinder the usefulness of such directional systems for problems in moderately high dimensions such as video processing. In this talk, we attack this problem by using directional tensor product complex tight framelets with mixed sampling factors. Such introduced directional system has good directionality with a very low redundancy rate 3d−12d−1, e.g., the redundancy rates are 2, 223, 357, 513 and 72531 for dimension d=1,…,5. Our numerical experiments on image/video denoising and inpainting show that the performance of our proposed directional system with low redundancy rate is comparable or better than several state-of-the-art methods which have much higher redundancy rates. In the second part, we shall discuss our recent developments of directional quasi-tight framelets in high dimensions. This is a joint work with Chenzhe Diao, Zhenpeng Zhao and Xiaosheng Zhuang. |
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