Sparse signal recovery from correlation measurements using the noise collector

The problem of sparse signal recovery from quadratic cross-correlation measurements is considered. Compared to the signal recovery problem that uses linear data, the unknown here is a matrix, X=\rho \rho^{\ast}, formed by the cross correlations of \rho, a K-dimensional vector that is the unknown of the linear problem. Solving for X creates a bottleneck as the number of unknowns grows now quadratically in K. To solve this problem efficiently a dimension reduction approach is proposed in which the contribution of the off-diagonal terms \rho{i} \rho{j}^{\ast} for \mathbf{i} \neq \mathbf{j} to the data is treated as noise and is absorbed using the Noise Collector [1]. With this approach, we recover the unknown X by solving a convex linear problem whose cost is similar to the one that uses linear measurements.

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Work Title Sparse signal recovery from correlation measurements using the noise collector
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Open Access
Creators
  1. Miguel Moscoso
  2. Alexei Novikov
  3. George Papanicolaou
  4. Chrysoula Tsogka
License In Copyright (Rights Reserved)
Work Type Article
Publication Date January 1, 2021
Publisher Identifier (DOI)
  1. https://doi.org/10.1109/CAMA49227.2021.9703482
Deposited September 19, 2022

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Version 1
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  • Created
  • Added Fast_Signal_Recovery_From_Quadratic_Measurements.pdf
  • Added Creator Miguel Moscoso
  • Added Creator Alexei Novikov
  • Added Creator George Papanicolaou
  • Added Creator Chrysoula Tsogka
  • Published
  • Updated