波传播反问题的理论分析、计算方法及应用

This proposal will investigate the propagation, scattering and inverse scattering of electromagnetic waves in complex medium. We will develop a class of basic algorithms and related computational models for computing large scale inverse problems in optics and electromagnetic waves. The study will be conducted in several folds including inverse scattering problem with incomplete data, multiscale inverse problems, computing electromagnetic waves with large wave number, near-field imaging, ill-posedness of inverse problems especially instability, uncertainty principle and so on. The new methods and algorithms will overcome some common ill-posedness of a large variety of inverse problems. The modeling and computational methods for inverse problems have far-range applications like nondestructive testing, geophysical imaging, underwater detection, life sicience, near-field imaging and nano-optics. This proposal will bring basic algorithms and computational modeling together for developing a new direction based upon uncertainty principle, which could be applied to solve common difficulties arise from inverse problems and make breakthroughs in theories, algorithms and modeling.

本项目将研究大规模复杂介质中光波与电磁波传播的散射和反散射问题。我们将发展一类新的基础算法及相关的可计算建模来求解光学与电磁场中的大规模反问题，内容包括不完全数据的反散射问题，大规模多尺度反问题计算，高波数下电磁波的传播问题，通过近场成像达到超分辨率，反问题的不适定性和稳定性，测不准原理和不可分辨性等。这类新的数值求解反散射问题的方法从理论上将克服反问题不适定性等著名共性难题。大规模的反散射问题的数值计算及相关建模不仅在科学、技术中有广泛应用，如无损探测、地质成像、水下探测、生命科学、近场及纳米光学，同时由于其代表性也为将来进一步研究其它各类包括声波、弹性波、量子波的波传播的反问题提供了基础。本项目的主要特色就是将基础算法与可计算建模相结合，发展基于测不准原理的新方法，解决相关共性难题，力争在理论、算法、建模及应用上取得突破。