一维相位恢复中的线性规范变换幅度的歧义
Ambiguities in one-dimensional phase retrieval from magnitudes of a linear canonical transform
AI总结：
本文研究了一维相位恢复问题，通过线性规范变换的幅度来恢复未知信号，并探讨了该问题中的歧义现象，将经典傅里叶相位恢复问题的解集特征转移到新设定中。
摘要：
相位恢复问题出现在物理和工程的广泛应用中。通常，这些问题涉及从信号的傅里叶变换的幅度中恢复未知信号。然而，在某些应用中，给定的强度来自于不同的变换，如菲涅耳或分数傅里叶变换。更一般地说，我们考虑从任意线性规范变换的幅度中恢复未知信号的相位恢复问题。利用傅里叶变换和线性规范变换之间的紧密关系，我们研究这些相位恢复问题中出现的歧义，并将已知的解集特征从经典的傅里叶相位恢复问题转移到新的设定中。
英文摘要：
Phase retrieval problems occur in a wide range of applications in physics and engineering. Usually, these problems consist in the recovery of an unknown signal from the magnitudes of its Fourier transform. In some applications, however, the given intensity arises from a different transformation such as the Fresnel or fractional Fourier transform. More generally, we here consider the phase retrieval of an unknown signal from the magnitudes of an arbitrary linear canonical transform. Using the close relation between the Fourier and the linear canonical transform, we investigate the arising ambiguities of these phase retrieval problems and transfer the well-known characterizations of the solution sets from the classical Fourier phase retrieval problem to the new setting.
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