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

这项研究涉及到一个迄今尚未解决的信号重建问题，即相位恢复。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，则出现仅从其幅度信息重建信号的困难问题。这项研究的目的是进一步发展新的基于多分辨率的相位恢复方法，并将其直接应用于实践和工程课堂。首席研究人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、互联网多媒体等的一项基本技术。此外，这项研究的教育举措包括：将以研究为基础的项目纳入本科生和研究生课程；利用协作学习和基于网络的教学工具；以及开展旨在招聘和留住工程学女性的活动。相位恢复在工程和应用物理的多个领域有着重要的应用，如：天线设计、天文学、仪器设计、电子显微镜和X射线结晶学。例如，在天线设计中，在非常高的频率(例如，在太赫兹制度下)测量天线的远场中的相位信息可能昂贵得令人望而却步。然而，重建发射天线的口径场分布需要相位信息。因此，仅从测量的幅度信息重建相位使得潜在的低成本天线测量成为可能。这项研究扩展了研究人员的新的相位恢复方法，通过他们的新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还导致了基于多分辨率的图像压缩的新结果--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.