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III, Estimating a signal from a magnitude spectrogram via convex optimization, Available online: arXiv:1209.2076 (0)

by D L Sun, J O Smith
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Sparse Phase Retrieval from Short-Time Fourier Measurements

by Yonina C. Eldar, Pavel Sidorenko, Dustin G. Mixon, Shaby Barel, Oren Cohen
"... Abstract—We consider the classical 1D phase retrieval problem. In order to overcome the difficulties associated with phase re-trieval from measurements of the Fourier magnitude, we treat recovery from the magnitude of the short-time Fourier trans-form (STFT). We first show that the redundancy offere ..."
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Abstract—We consider the classical 1D phase retrieval problem. In order to overcome the difficulties associated with phase re-trieval from measurements of the Fourier magnitude, we treat recovery from the magnitude of the short-time Fourier trans-form (STFT). We first show that the redundancy offered by the STFT enables unique recovery for arbitrary nonvanishing inputs, under mild conditions. An efficient algorithm for recovery of a sparse input from the STFT magnitude is then suggested, based on an adaptation of the recently proposed GESPAR algorithm. We demonstrate through simulations that using the STFT leads to improved performance over recovery from the oversampled Fourier magnitude with the same number of measurements. Index Terms—GESPAR, phase retrieval, short-time Fourier transform, sparsity.
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...FT magnitude of the measured pulse [23], [12]. Another example is ptychographical CDI [8]. Both Fienup-type methods [7], [12] and SDP approaches have been extended to recovery from the STFT magnitude =-=[22]-=-. Here, we first show that the redundancy offered by the STFT enables unique recovery for arbitrary inputs that are nonvanishing, under mild conditions. We then suggest an efficient algorithm for reco...

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by Aaron A. Nelson, D Lt, Aaron A. Nelson, D Lt, Aaron A. Nelson, D Lt, Benjamin F. Akers, Jesse D. Peterson , 2014
"... or the United States Government. This material is declared a work of the U.S. ..."
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or the United States Government. This material is declared a work of the U.S.
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...verting the STFT using the (noisy) unaltered phases of the coefficients, one can recover the denoised version of the signal by first discarding the phases and then reconstructing with phase retrieval =-=[8, 85]-=-. Although there are many applications of phase retrieval, the task is often impossible. For instance, intensity measurements with the identity basis effectively discard the phase information of a sig...

Phase Transitions in Phase Retrieval

by Dustin G. Mixon , 2014
"... ..."
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...nsform (STFT) and perform a smoothing operation on the magnitudes of the coefficients [5]. Instead of inverting the STFT with the noisy phases, one can recover the denoised version by phase retrieval =-=[49]-=-. Though there are many applications of phase retrieval, the task is often impossible; in particular, discarding the phases of the Fourier transform is not at all injective. This fact has led many res...

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