具有充分断开支持的函数的相位检索

T. Crimmins, J. Fienup
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引用次数: 63

摘要

相位恢复的问题是从函数f(x)的傅里叶变换的模| f(u)|重建函数f(x),这相当于从| f(u)|重建f(u)的相位,或者从它的自相关函数重建f(x),它由| f(u)|2的反傅里叶变换给出。这个问题出现在许多领域,包括天文学、x射线晶体学、波前传感、瞳孔功能测定、电子显微镜和粒子散射。本文假设函数f是一个平方可积的一维复值函数。如果f在满足一定分离条件的区间序列的并集中有不连通的紧支持,则可以证明f几乎总是那些区间的并集中包含支持的唯一解。不管F有多少个非实数0,这个都成立。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Phase Retrieval for Functions with Sufficiently Disconnected Support
The problem of phase retrieval is to reconstruct a function, f(x),from the modulus, |F(u)|, of its Fourier transform, This is equivalent to reconstructing the phase of F(u) from |F(u)| or to reconstructing f(x) from its autocorrelation function, which is given by the in verse Fourier transform of |F(u)|2. This problem arises in many fields, including astronomy, x-ray crystallography, wavefront sensing, pupil function determination, electron microscopy, and particle scattering. In this paper the function, f, is assumed to be a square-integrable, one-dimensional, complex-valued function. If f has disconnected compact support contained in the union of a sequence of intervals satisfying a certain separation condition, then it can be shown that f is almost always essentially the only solution with support contained in the union of those intervals. This holds no matter how many non-real zeroes F has.
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