Phase Retrieval for $L^2([-\pi,\pi])$ via the Provably Accurate and Noise Robust Numerical Inversion of Spectrogram Measurements
Phase Retrieval for $L^2([-\pi,\pi])$ via the Provably Accurate and Noise Robust Numerical Inversion of Spectrogram Measurements
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通过可证明准确且抗噪的频谱图测量数值反演来检索 $L^2([-pi,pi])$
DOI：
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发表时间：
2021
期刊：
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通讯作者：
A. Viswanathan
中科院分区：
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作者：
M. Iwen;Michael Perlmutter;N. Sissouno;A. Viswanathan
在这篇文章中，我们集中于从一组有限的短时傅里叶变换(STFT)幅度(即谱图)测量中，对光滑函数$f：[-\pi，\pi]\right tarrow\mathbb{C}$的逼近，直到无法分辨的全局相位模糊。开发了两种算法来近似反转这种测量，每一种算法都具有理论误差，保证了它们的正确性。详细的数值研究还表明，这两种算法在实际应用中效果都很好，并且具有良好的数值收敛行为。
In this paper, we focus on the approximation of smooth functions $f: [-\pi, \pi] \rightarrow \mathbb{C}$, up to an unresolvable global phase ambiguity, from a finite set of Short Time Fourier Transform (STFT) magnitude (i.e., spectrogram) measurements. Two algorithms are developed for approximately inverting such measurements, each with theoretical error guarantees establishing their correctness. A detailed numerical study also demonstrates that both algorithms work well in practice and have good numerical convergence behavior.