Phase Retrieval from Linear Canonical Transforms

IF 1.4 4区数学 Q2 MATHEMATICS, APPLIED

Numerical Functional Analysis and Optimization Pub Date : 2022-10-19 DOI:10.1080/01630563.2022.2132511

Yang Chen, Na Qu

引用次数: 1

Abstract

Abstract The classical phase retrieval problem aims to recover an unknown function from the Fourier magnitudes. The linear canonical transform has a more generalized form of the well-known (fractional) Fourier transform and a wide range of engineering applications such as optics and quantum mechanism. In this paper, we consider the linear canonic phase retrieval problem of determining a function from the magnitudes of the linear canonic transforms. We show that a compactly supported function f can be determined, up to a global phase, from the magnitudes of multiple linear canonic transforms, where is a class of real unimodular matrices. It generalizes the results of phase retrieval from multiple fractional Fourier transforms. On the other hand, we show that a compactly supported function f can be determined, up to a global phase, from the interference linear canonic magnitudes and where Moreover, if the ambiguity of conjugate reflection is taken into account, the compactly supported function f can be determined, up to a rotation and conjugate reflection, from the linear canonic magnitudes and

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基于线性正则变换的相位检索

经典相位恢复问题旨在从傅里叶幅值中恢复未知函数。线性正则变换是傅里叶变换的一种更广义的形式，在光学和量子力学等领域有着广泛的应用。本文研究了由线性正则变换的幅度确定函数的线性正则相位恢复问题。我们证明了一个紧支持函数f可以由多个线性正则变换的模来确定，直到一个全局相位，其中是一类实非模矩阵。推广了多次分数阶傅里叶变换的相位恢复结果。另一方面，我们证明了紧支持函数f可以从干涉的线性模量确定到一个全局相位，并且，如果考虑到共轭反射的模糊性，则可以从线性模量和确定到一个旋转和共轭反射的紧支持函数f

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Numerical Functional Analysis and Optimization 数学-应用数学

CiteScore

2.40

自引率

8.30%

发文量

审稿时长

6-12 weeks

期刊介绍： Numerical Functional Analysis and Optimization is a journal aimed at development and applications of functional analysis and operator-theoretic methods in numerical analysis, optimization and approximation theory, control theory, signal and image processing, inverse and ill-posed problems, applied and computational harmonic analysis, operator equations, and nonlinear functional analysis. Not all high-quality papers within the union of these fields are within the scope of NFAO. Generalizations and abstractions that significantly advance their fields and reinforce the concrete by providing new insight and important results for problems arising from applications are welcome. On the other hand, technical generalizations for their own sake with window dressing about applications, or variants of known results and algorithms, are not suitable for this journal. Numerical Functional Analysis and Optimization publishes about 70 papers per year. It is our current policy to limit consideration to one submitted paper by any author/co-author per two consecutive years. Exception will be made for seminal papers.