图 书 馆
图形模型和应用Graphical Models and Applications |
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| 课程网址: | http://videolectures.net/mlss09us_weiss_gma/ |
| 主讲教师: | Yair Weiss |
| 开课单位: | 耶路撒冷希伯来大学 |
| 开课时间: | 2009-07-30 |
| 课程语种: | 英语 |
| 中文简介: |  |
| 课程简介: | Compressed sensing is a recent set of mathematical results showing that sparse signals can be exactly reconstructed from a small number of linear measurements. Interestingly, for ideal sparse signals with no measurement noise, random measurements allow perfect reconstruction while measurements based on principal component analysis (PCA) or independent component analysis (ICA) do not. At the same time, for other signal and noise distributions, PCA and ICA can significantly outperform random projections in terms of enabling reconstruction from a small number of measurements. In this paper we ask: given a training set typical of the signals we wish to measure, what are the optimal set of linear projections for compressed sensing? We show that the optimal projections are in general not the principal components nor the independent components of the data, but rather a seemingly novel set of projections that capture what is still uncertain about the signal, given the training set. We also show that the projections onto the learned uncertain components may far outperform random projections. This is particularly true in the case of natural images, where random projections have vanishingly small signal to noise ratio as the number of pixels becomes large. Joint work with Hyun-Sung Chang and Bill Freeman. I will give a brief introduction to questions of representation, learning and inference in probabilistic graphical models and illustrate these ideas in applications from our own work in computational biology and computer vision. |
| 关 键 词: | 压缩感知; 线性测量; 测量噪声 |
| 课程来源: | 视频讲座网 |
| 最后编审: | 2019-07-23：cwx |
| 阅读次数: | 31 |