Solving complex quadratic systems with full-rank random matrices

Huang, Shuai and Gupta, Sidharth and Dokmanić, Ivan. (2020) Solving complex quadratic systems with full-rank random matrices. IEEE Transactions on Signal Processing, 68. pp. 4782-4796.

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Official URL: https://edoc.unibas.ch/81803/

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We tackle the problem of recovering a complex signal x ∈ Cn from quadratic measurements of the form yi = x*A i x, where Ai is a full-rank, complex random measurement matrix whose entries are generated from a rotation-invariant sub-Gaussian distribution. We formulate it as the minimization of a nonconvex loss. This problem is related to the well understood phase retrieval problem where the measurement matrix is a rank-1 positive semidefinite matrix. Here we study the general full-rank case which models a number of key applications such as molecular geometry recovery from distance distributions and compound measurements in phaseless diffractive imaging. Most prior works either address the rank-1 case or focus on real measurements. The several papers that address the full-rank complex case adopt the computationally-demanding semidefinite relaxation approach. In this paper we prove that the general class of problems with rotation-invariant sub-Gaussian measurement models can be efficiently solved with high probability via the standard framework comprising a spectral initialization followed by iterative Wirtinger flow updates on a nonconvex loss. Numerical experiments on simulated data corroborate our theoretical analysis.
Faculties and Departments:05 Faculty of Science > Departement Mathematik und Informatik > Informatik > Signal and Data Analytics (Dokmanic)
UniBasel Contributors:Dokmanić, Ivan
Item Type:Article, refereed
Article Subtype:Research Article
Note:Publication type according to Uni Basel Research Database: Journal article
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Last Modified:20 Oct 2021 12:10
Deposited On:20 Oct 2021 12:10

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