Invertibility and robustness of phaseless reconstruction

DOI10.1016/j.acha.2014.07.003zbMath1337.42032arXiv1308.4718OpenAlexW2963882048MaRDI QIDQ2343253

Yang Wang, Radu Balan

Publication date: 4 May 2015

Published in: Applied and Computational Harmonic Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1308.4718

zbMATH Keywords

framesphase retrievalredundant representationsphaseless reconstruction

Mathematics Subject Classification ID

Nontrigonometric harmonic analysis involving wavelets and other special systems (42C40) Signal theory (characterization, reconstruction, filtering, etc.) (94A12)

Related Items (21)

Lipschitz Analysis of Generalized Phase Retrievable Matrix Frames ⋮ On the stability of Fourier phase retrieval ⋮ Reconstruction of signals from magnitudes of redundant representations: the complex case ⋮ Phase retrieval of real-valued signals in a shift-invariant space ⋮ Phase retrieval from the magnitudes of affine linear measurements ⋮ Stable phase retrieval and perturbations of frames ⋮ Phase Retrieval: Uniqueness and Stability ⋮ Phase retrieval for the Cauchy wavelet transform ⋮ Robustness properties of dimensionality reduction with Gaussian random matrices ⋮ Phase retrievable projective representation frames for finite abelian groups ⋮ FROG-measurement based phase retrieval for analytic signals ⋮ \( \alpha \)-phase retrieval frame in Hilbert space and its application ⋮ Phase-retrievable operator-valued frames and representations of quantum channels ⋮ Phaseless reconstruction from space-time samples ⋮ Real phase retrieval from unordered partial frame coefficients ⋮ On Lipschitz analysis and Lipschitz synthesis for the phase retrieval problem ⋮ Phase retrieval in infinite-dimensional Hilbert spaces ⋮ On stability of generalized phase retrieval and generalized affine phase retrieval ⋮ On stability of generalized (affine) phase retrieval in the complex case ⋮ Signal reconstruction without phase by norm retrievable frames ⋮ Frame phase-retrievability and exact phase-retrievable frames

Uses Software

• PhaseLift

Cites Work

• Painless reconstruction from magnitudes of frame coefficients
• The art of frame theory
• Random matrices and erasure robust frames
• Saving phase: injectivity and stability for phase retrieval
• Phase retrieval: stability and recovery guarantees
• On signal reconstruction without phase
• Phase recovery, MaxCut and complex semidefinite programming
• PhaseLift: Exact and Stable Signal Recovery from Magnitude Measurements via Convex Programming
• Phase Retrieval via Matrix Completion

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