图 书 馆
傅里叶数据的最佳压缩成像Optimal compressive imaging for Fourier data |
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| 课程网址: | http://videolectures.net/sahd2014_kutyniok_fourier_data/ |
| 主讲教师: | Gitta Kutyniok |
| 开课单位: | 德国柏林数学研究所 |
| 开课时间: | 2014-10-29 |
| 课程语种: | 英语 |
| 中文简介: |  应用数学中的一个基本问题是从特定样本中恢复数据的问题。尤其重要的是相关联的傅立叶变换的逐点采样的情况，例如，这些采样是在磁共振成像（MRI）中收集的。因此，以规定的精度减少重建所需的样本数量的策略直接影响了此类应用{在MRI的情况下，例如，这将缩短患者被迫躺在扫描仪中的时间。在本次演讲中，我们将提出傅里叶样本的稀疏二次采样策略，该策略可以证明对各向异性特征控制的函数具有最佳性能。为此，我们将介绍一种可重构的对偶剪枝框架，该框架可提供此类功能的可证明的最佳稀疏近似值（这类卡通图像通常被视为图像的合适模型。考虑到傅立叶基础和小波框架之间的相干性，采样方案将基于压缩感测思想并结合相干性自适应采样密度。我们最终证明，这种通用采样策略可以从具有最佳采样率的傅立叶样本集合中稀疏地近似所考虑的模型类的功能。 |
| 课程简介: | One fundamental problem in applied mathematics is the issue of recovery of data from speci c samples. Of particular importance is the case of pointwise samples of the associated Fourier transform, which are, for instance, collected in Magnetic Resonance Imaging (MRI). Strategies to reduce the number of samples required for reconstruction with a prescribed accuracy have thus a direct impact on such applications { which in the case of MRI will, for instance, shorten the time a patient is forced to lie in the scanner. In this talk, we will present a sparse subsampling strategy of Fourier samples which can be shown to perform optimally for functions governed by anisotropic features. For this, we will introduce a dualizable shearlet frame for reconstruc- tion, which provides provably optimally sparse approximations of this class of functions { such cartoon-like images are typically regarded as a suitable model for images. The sampling scheme will be based on compressive sensing ideas combined with a coherence-adaptive sampling density considering the coherence between the Fourier basis and the shearlet frame. We nally prove that this general sampling strategy can sparsely approximate a function of the consid- ered model class from a collection of its Fourier samples with optimal sampling rate. |
| 关 键 词: | 傅里叶模型; 压缩技术 |
| 课程来源: | 视频讲座网 |
| 数据采集: | 2020-10-12：zyk |
| 最后编审: | 2020-10-12：zyk |
| 阅读次数: | 56 |