An algorithm for exact super-resolution and phase retrieval

Chen, Yuxin; Eldar, Yonina C.; Goldsmith, Andrea

doi:10.1109/icassp.2014.6853697

Cited by 8 publications

(6 citation statements)

References 39 publications

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“…An extension to the continuous setup was suggested in [39]. A combinatorial algorithm for recovering a signal from its low-resolution Fourier magnitude was suggested in [38]. The algorithm recovers an s-sparse signal exactly from 2s 2 − 2s + 2 lowpass magnitudes.…”

Section: Algorithms For Sparse Signalsmentioning

confidence: 99%

Fourier Phase Retrieval: Uniqueness and Algorithms

Bendory

Beinert

Eldar

2017

Compressed Sensing and Its Applications

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The problem of recovering a signal from its phaseless Fourier transform measurements, called Fourier phase retrieval, arises in many applications in engineering and science. Fourier phase retrieval poses fundamental theoretical and algorithmic challenges. In general, there is no unique mapping between a one-dimensional signal and its Fourier magnitude and therefore the problem is ill-posed. Additionally, while almost all multidimensional signals are uniquely mapped to their Fourier magnitude, the performance of existing algorithms is generally not well-understood. In this chapter we survey methods to guarantee uniqueness in Fourier phase retrieval. We then present different algorithmic approaches to retrieve the signal in practice. We conclude by outlining some of the main open questions in this field.

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Section: Algorithms For Sparse Signalsmentioning

confidence: 99%

Fourier Phase Retrieval: Uniqueness and Algorithms

Bendory

Beinert

Eldar

2017

Compressed Sensing and Its Applications

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“…of multidimensional spike models [2] and antenna array design [26]. Thus, a better understanding of MHR will also lead to more insights in a wide range of problems in signal processing.…”

mentioning

confidence: 99%

Multidimensional Harmonic Retrieval via Coupled Canonical Polyadic Decomposition—Part I: Model and Identifiability

Sørensen

Lathauwer

2017

IEEE Trans. Signal Process.

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Multidimensional Harmonic Retrieval (MHR) is a fundamental problem in signal processing. We make a connection with coupled Canonical Polyadic Decomposition (CPD), which allows us to better exploit the rich MHR structure than existing approaches in the derivation of uniqueness results. We discuss both deterministic and generic conditions. We obtain a deterministic condition that is both necessary and sufficient but which may be difficult to check in practice. We derive mild deterministic relaxations that are easy to verify. We also discuss the variant in which the generators have unit norm. We narrow the transition zone between generic uniqueness and generic non-uniqueness to two values of the number of harmonics. We explain differences with one-dimensional HR.Index Terms-coupled canonical polyadic decomposition, tensor, Vandermonde matrix, multidimensional harmonic retrieval. I. IntroductionDuring the past two decades Multidimensional Harmonic Retrieval (MHR) has become an important problem in signal processing. MHR is a fundamental problem that appears in a wide range of applications in traditional signal processing, such as radar, sonar, wireless communication and channel sounding, see [32], [16], [19], [24], [22], [23], [13], [37] and references therein. The MHR structure can be due to Doppler effects, structured receive and/or transmit antenna arrays, sinusoidal carriers, carrier frequency off-sets, and so on. Another classical signal processing application of MHR is multidimensional NMR spectroscopy (e.g. [21]). More recent MHR applications in signal processing include sampling of parametric nonbandlimited 2D signals [25], phase retrieval of parametric 2D signals [31], phase retrieval

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“…Super-resolving a signal from only magnitudes of lowfrequency Fourier measurements is often ill-posed due to lack of both phase information and high-frequency information; and hence it is a challenging problem. The authors in [1,12] considered the phaseless super-resolution aiming at recovering signals with only low-frequency magnitude measurements. In the noiseless setting, the authors in [12] proposed a combinatorial algorithm for signal recovery using only lowfrequency Fourier magnitude measurements, but this algorithm requires additional distinguishing conditions on the signal impulses.…”

Section: Introductionmentioning

confidence: 99%

Phaseless super-resolution in the continuous domain

Cho

Thrampoulidis

et al. 2017

2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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Phaseless super-resolution refers to the problem of superresolving a signal from only its low-frequency Fourier magnitude measurements. In this paper, we consider the phaseless super-resolution problem of recovering a sum of sparse Dirac delta functions which can be located anywhere in the continuous time-domain. For such signals in the continuous domain, we propose a novel Semidefinite Programming (SDP) based signal recovery method to achieve the phaseless superresolution. This work extends the recent work of Jaganathan et al. [1], which considered phaseless super-resolution for discrete signals on the grid.

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An algorithm for exact super-resolution and phase retrieval

Cited by 8 publications

References 39 publications

Fourier Phase Retrieval: Uniqueness and Algorithms

Fourier Phase Retrieval: Uniqueness and Algorithms

Multidimensional Harmonic Retrieval via Coupled Canonical Polyadic Decomposition—Part I: Model and Identifiability

Phaseless super-resolution in the continuous domain

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