Phase Retrieval for L^2([-π,π]) via the Provably Accurate and Noise Robust Numerical Inversion of Spectrogram Measurements
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In this paper, we focus on the approximation of smooth functions f: [-π, π] →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.
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