Measurement matrix design for phase retrieval based on mutual information

Nir Shlezinger, Ron Dabora, Yonina C. Eldar

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


In phase retrieval problems, a signal of interest (SOI) is reconstructed based on the magnitude of a linear transformation of the SOI observed with additive noise. The linear transform is typically referred to as a measurement matrix. Many works on phase retrieval assume that the measurement matrix is a random Gaussian matrix, which, in the noiseless scenario with sufficiently many measurements, guarantees invertability of the transformation between the SOI and the observations, up to an inherent phase ambiguity. However, in many practical applications, the measurement matrix corresponds to an underlying physical setup, and is therefore deterministic, possibly with structural constraints. In this paper, we study the design of deterministic measurement matrices, based on maximizing the mutual information between the SOI and the observations. We characterize necessary conditions for the optimality of a measurement matrix, and analytically obtain the optimal matrix in the low signal-to-noise ratio regime. Practical methods for designing general measurement matrices and masked Fourier measurements are proposed. Simulation tests demonstrate the performance gain achieved by the suggested techniques compared to random Gaussian measurements for various phase recovery algorithms.

Original languageEnglish
Pages (from-to)324-339
Number of pages16
JournalIEEE Transactions on Signal Processing
Issue number2
StatePublished - 15 Jan 2018


  • Masked fourier
  • Measurement matrix design
  • Mutual information
  • Phase retrieval

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering


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