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

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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.