TY - JOUR
T1 - Recent Advances in Phase Retrieval
AU - Eldar, Yonina C.
AU - Hammen, Nathaniel
AU - Mixon, Dustin G.
N1 - The work of Yonina C. Eldar was funded by the European Unions Horizon 2020 research and innovation programme under grant agreement ERC-BNYQ, by the Israel Science Foundation under grant 335/14, and by ICore: the Israeli Excellence Center Circle of Light. The work of Nathaniel Hammen and Dustin G. Mixon was funded by an Air Force Office of Scientific Research (AFOSR) Young Investigator Research Program award, National Science Foundation grant DMS-1321779, and AFOSR grant F4FGA05076J002. Nathaniel Hammen was also supported in part by an appointment to the Postgraduate Research Participation Program at the U.S. Air Force Institute of Technology, administered by the Oak Ridge Institute for Science and Education through an interagency agreement between the U.S. Department of Energy and the Air Force Institute of Technology. The views expressed in this article are those of the authors and do not reflect the official policy or position of the United States Air Force, Department of Defense, or the U.S. Government.
PY - 2016/9
Y1 - 2016/9
N2 - In many applications in science and engineering, one is given the modulus squared of the Fourier transform of an unknown signal and then tasked with solving the corresponding inverse problem, known as phase retrieval. Solutions to this problem have led to some noteworthy accomplishments, such as identifying the double helix structure of DNA from diffraction patterns, as well as characterizing aberrations in the Hubble Space Telescope from point spread functions. Recently, phase retrieval has found interesting connections with algebraic geometry, low-rank matrix recovery, and compressed sensing. These connections, together with various new imaging techniques developed in optics, have spurred a surge of research into the theory, algorithms, and applications of phase retrieval. In this lecture note, we outline these recent connections and highlight some of the main results in contemporary phase retrieval.
AB - In many applications in science and engineering, one is given the modulus squared of the Fourier transform of an unknown signal and then tasked with solving the corresponding inverse problem, known as phase retrieval. Solutions to this problem have led to some noteworthy accomplishments, such as identifying the double helix structure of DNA from diffraction patterns, as well as characterizing aberrations in the Hubble Space Telescope from point spread functions. Recently, phase retrieval has found interesting connections with algebraic geometry, low-rank matrix recovery, and compressed sensing. These connections, together with various new imaging techniques developed in optics, have spurred a surge of research into the theory, algorithms, and applications of phase retrieval. In this lecture note, we outline these recent connections and highlight some of the main results in contemporary phase retrieval.
U2 - https://doi.org/10.1109/MSP.2016.2565061
DO - https://doi.org/10.1109/MSP.2016.2565061
M3 - كلمة العدد
SN - 1053-5888
VL - 33
SP - 158
EP - 162
JO - IEEE Signal Processing Magazine
JF - IEEE Signal Processing Magazine
IS - 5
ER -