In this talk I will focus on the approximation of smooth functions, up to an unresolvable global phase ambiguity, from a finite set of Short Time Fourier Transform (STFT) magnitude (i.e., spectrogram) measurements. Algorithms are developed for approximately inverting such measurements, each with theoretical error guarantees establishing their correctness. A detailed empirical study further demonstrates that the algorithms work well in practice and have good numerical convergence behavior. Theoretical implications concerning the solution of realistic ptychographic imaging problems via neural networks will also be discussed.
This is joint work with Mike Perlmutter (UCLA), Nada Sissouno (TUM), and Aditya Viswanathan (UM-Dearborn)
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