On signal reconstruction without phase

By Radu V. Balan, Peter G. Casazza, Dan Edidin. 2006

630 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computer Vision and Pattern Recognition, Signal Processing

View Paper: https://www.semanticscholar.org/paper/43f2540490562cfd7ade43e74d088973973a22ba

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In Applied Mathematics

In Computer Vision and Pattern Recognition

In Signal Processing

Citations in the corpus

Phase Retrieval via Wirtinger Flow: Theory and Algorithms (2014, methodology): “Because of the practical significance of the phase retrieval problem in imaging science, the community has developed methods for recovering a signal x ∈ Cn from data of the form yr = ∣⟨ar,x⟩∣2 in the special case where one samples the (square) modulus of its Fourier transform.”
A Geometric Analysis of Phase Retrieval (2016, background): “4Another line of research [23–25] seeks to co-design the measurements and recovery algorithms based on frame- or graph-theoretic tools.”
Statistical guarantees for the EM algorithm: From population to sample-based analysis (2014, neutral): “, [3, 9, 35]).”
Phase Retrieval from Coded Diffraction Patterns (2013, neutral): “Other areas where related problems appear include acoustics [12, 8], blind channel estimation in wireless communications [4, 45], interferometry [28], quantum mechanics [25, 47] and quantum information [34].”
Signal recovery from Pooling Representations (2013, background): “As in previous works on compressed sensing (Candes and Tao, 2004) and phase recovery (Balan et al., 2006), one may address this question by studying random pooling operators.”
Phase Retrieval with Application to Optical Imaging: A contemporary overview (2015, background): “The work of Balan [40] implies that, for real signals in , R N 2 1 - random measurements are needed, provided that they are full spark, i.”
An Overview of Low-Rank Matrix Recovery From Incomplete Observations (2016, background): “In [118], it is shown that for generic a , if L ≥ 2N − 1, then v0 is the only vector (up to a sign) that has the measurements (26).”
Saving phase: Injectivity and stability for phase retrieval (2013, methodology): “In the real case, the complement property is characteristic of injectivity, as demonstrated in [7].”
A new identity for Parseval frames (2007, methodology): “While working on efficient algorithms for signal reconstruction, the authors of [1] discovered a surprising identity for Parseval frames (see [2] for a detailed discussion of the origins of the identity).”
Unsupervised Deep Haar Scattering on Graphs (2014, background): “airing problem. A scattering S J operators is not invertible because the modulus looses a complex phase or a sign. In the real case, for almost all pairs of unitary operators (A;B) it has been proved [11] that the operator (jAj;jBj) is invertible on Rd. If Wis real, one can thus expect that (jWˇ0j;j”
Compressive phase retrieval via generalized approximate message passing (2012, background): “Non-imaging applications include acoustics [12], interferometry [13], and quantum mechanics [14].”
An Introduction to Frames (2008, background): “1 No one seems to know why they are called frames, perhaps because of the bounds in (3.8).”