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Stable Recovery from the Magnitude of Symmetrized Fourier Measurements by Walk, Philipp; Jung, Peter is a scholarly article available to read on EtoBox.

What is Stable Recovery from the Magnitude of Symmetrized Fourier Measurements about?

In this note we show that stable recovery of complex-valued signals $x\in\mathbb{C}^n$ up to global sign can be achieved from the magnitudes of $4n-1$ Fourier measurements when a certain "symmetrization and zero-padding" is performed before measurement ($4n-3$ is possible in certain cases). For real signals, symmetrization itself is linear and therefore our result is in this case a statement on uniform phase retrieval. Since complex conjugation is involved, such measurement procedure is not complex-linear but recovery is still possible from magnitudes of linear measurements on, for example, $(\Re(x),\Im(x))$.

Author

Walk, Philipp; Jung, Peter

Published

2013

Language

EN