CAREER: Multiresolution-Based Continuous Phase Retrieval: Theory and Applications

本研究涉及到一个迄今为止尚未解决的信号重建问题——相位恢复。一个信号——如心电图、图像或视频——可以用幅度和相位信息来表示。然而，如果相位信息不可用，仅从其幅度信息重建信号的难题就出现了。本研究的目的是进一步发展新的基于多分辨率的相位检索方法，并将其直接应用于实践和工程课堂。首席研究员还将这些基于多分辨率的技术应用于图像压缩，这是无线通信、数字图像库、互联网多媒体等的基本技术。此外，本研究的教育倡议包括：将研究性项目纳入本科和研究生课程；利用协作学习和网络教学工具；开展旨在招募和留住工程领域女性的活动。相位反演在工程和应用物理的许多领域都有重要的应用，例如：天线设计、天文学、仪器设计、电子显微镜和x射线晶体学。例如，在天线设计中，天线远场相位信息的测量在非常高的频率下（例如在太赫兹频段）可能会非常昂贵。然而，相位信息是重建发射天线孔径场分布所必需的。因此，仅从测量的幅度信息重建相位可以实现潜在的低成本天线测量。本研究扩展了研究者的新相位检索方法，通过其新颖的多分辨率方法为以前无法解决的问题提供解决方案。首席研究员正在进行的研究也在基于多分辨率的图像压缩方面取得了新的成果，这种协同关系将在整个研究项目中继续发展。

This research involves a heretofore unsolved signal reconstruction problem called phase retrieval. A signal--such as an electrocardiogram, an image, or video--can be represented in terms of magnitude and phase information. However if the phase information is unavailable, the difficult problem of reconstructing the signal from only its magnitude information arises. The objective of this research is to further develop new multiresolution-based phase retrieval methods and to transfer them directly into practice and into the engineering classroom. The principal investigator is also applying these multiresolution-based techniques to image compression--an essential technology for wireless communications, digital image libraries, multimedia over the Internet, etc. Furthermore, the educational initiatives of this research include: incorporating research-based projects into undergraduate and graduate courses; utilizing collaborative learning and web-based teaching tools; and, conducting activities designed to recruit and retain women in engineering. Phase retrieval has important applications in several areas of engineering and applied physics, such as: antenna design, astronomy, instrumentation design, electron microscopy, and x-ray crystallography. For instance in antenna design, the measurement of phase information in the far field of an antenna can be prohibitively expensive at very high frequencies (e.g. in the terahertz regime). However, the phase information is necessary for reconstructing the transmitting antenna's aperture field distribution. Thus, the reconstruction of phase from only the measured magnitude information enables potentially low cost antenna measurements. This research extends the investigator's new phase retrieval methods that provide solutions to previously unsolvable problems through their novel multiresolution approach. The principal investigator's on-going research has also led to new results in multiresolution-based image compression--a synergistic relationship that will continue to develop throughout this research project.