在一个先里面有什么? 学习了用于反向问题的近接网络
Zhenghan Fang1, Sam Buchanan2, Jeremias Sulam1
1Mathematical Institute for Data Science Johns Hopkins University.
概括
本研究介绍了反向问题的学习近位网络 (LPN),为数据驱动的调整器提供了精确的近位运算符. 一种新的近似匹配策略确保了趋同,并揭示了先前的学习数据.
科学领域:
- 计算机成像成像技术
- 机器学习用于反向问题.
- 优化理论就是优化理论.
背景情况:
- 靠近运算符对于规范化错误的反向问题至关重要.
- 深度学习模型 (plug-and-play,深度解滚) 接近近位运算符,但缺乏理论保证.
- 目前的数据驱动方法阻碍了趋同分析和了解已知的先验.
研究的目的:
- 引入学习近接网络 (LPN) 的框架.
- 证明LPN给出了数据驱动调整器的精确近位运算符.
- 制定培训策略 (近距离匹配) 以恢复数据分布的先行情况.
主要方法:
- 开发了学习近接网络 (LPN) 的框架.
- 为LPNs作为精确的近邻运营商提供了已证明的理论保证.
- 介绍并分析了近似匹配培训策略.
主要成果:
- 学习近位网络 (LPN) 为非凸规调整器提供了准确的近位运算符.
- 接近匹配训练可以证明恢复数据分布的日志前值.
- 对于反向问题,LPN提供了一般的,无监督的和有表达性的近位运算符.
结论:
- 在反向问题中,LPN为近位运算符提供了一个原则性的深度学习方法.
- 靠近性匹配策略可以保证趋同和可解释的先前学习.
- 从数据中展示了最先进的性能和对先前学习的洞察力.
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