Frame Theory And Its 应用程序s

Since its introduction in the early 1950’s, Hilbert space frame theory has become an active area of research due to its applications in engineering 和 physics, including in speech recognition, 光学成像, 和 X-ray crystallography. 帧, like orthonor-mal bases, 给出一个连续式, 线性, 和 stable reconstruction formula for vectors in a Hilbert space. 然而, frames allow for redundancy, 和 this makes frames much more adaptable for theory 和 applications. Phase retrieval is one of the applications of frame theory in which only the intensity of each 线性 measurement of a signal is available 和 the phase information is lost. In 2006, 巴兰, Casazza, 和 Edidin introduced a more powerful notion of phase retrieval using the magnitude of frame coefficients. Closely related to the subject of phase retrieval is 弱相位恢复. Weakening the con-ditions of phase retrieval, in which we have fewer measurements, still satisfies most of the properties of phase retrieval. In other words it is not “weak” at all. In this talk, we give an overview of phase retrieval 和 弱相位恢复. 除了, a review of current phase retrieval algorithms will be discussed; however, an algorithm for 弱相位恢复 has yet to be established.