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arXiv · 1909.02078

Phase retrieval of complex and vector-valued functions

Yang Chen·Cheng Cheng·Qiyu Sun
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Abstract

The phase retrieval problem in the classical setting is to reconstruct real/complex functions from the magnitudes of their Fourier/frame measurements. In this paper, we consider a new phase retrieval paradigm in the complex/quaternion/vector-valued setting, and we provide several characterizations to determine complex/quaternion/vector-valued functions $f$ in a linear space $S$ of (in)finite dimensions, up to a trivial ambiguity, from the magnitudes $\|\phi(f)\|$ of their linear measurements $\phi(f), \phi\in \Phi$. Our characterization in the scalar setting implies the well-known equivalence between the complement property for linear measurements $\Phi$ and the phase retrieval of linear space $S$. In this paper, we also discuss the affine phase retrieval of vector-valued functions in a linear space and the reconstruction of vector fields on a graph, up to an orthogonal matrix, from their absolute magnitudes at vertices and relative magnitudes between neighboring vertices.

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Yang Chen, Cheng Cheng, Qiyu Sun. 2019-09-04. Phase retrieval of complex and vector-valued functions. https://arxiv.org/abs/1909.02078

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