Blind Gain and Phase Calibration via Sparse Spectral Methods

Yanjun Li, Kiryung Lee, Yoram Bresler

Research output: Contribution to journalArticlepeer-review


Blind gain and phase calibration (BGPC) is a bilinear inverse problem involving the determination of unknown gains and phases of the sensing system, and the unknown signal, jointly. BGPC arises in numerous applications, e.g., blind albedo estimation in inverse rendering, synthetic aperture radar autofocus, and sensor array auto-calibration. In some cases, sparse structure in the unknown signal alleviates the ill-posedness of BGPC. Recently, there has been renewed interest in solutions to BGPC with careful analysis of error bounds. In this paper, we formulate BGPC as an eigenvalue/eigenvector problem and propose to solve it via power iteration, or in the sparsity or joint sparsity case, via truncated power iteration. Under certain assumptions, the unknown gains, phases, and the unknown signal can be recovered simultaneously. Numerical experiments show that power iteration algorithms work not only in the regime predicted by our main results, but also in regimes where theoretical analysis is limited. We also show that our power iteration algorithms for BGPC compare favorably with competing algorithms in adversarial conditions, e.g., with noisy measurement or with a bad initial estimate.

Original languageEnglish (US)
Article number8550743
Pages (from-to)3097-3123
Number of pages27
JournalIEEE Transactions on Information Theory
Issue number5
StatePublished - May 2019
Externally publishedYes


  • Auto-calibration
  • SAR autofocus
  • greedy algorithm
  • inverse rendering
  • multichannel blind deconvolution
  • nonconvex optimization
  • power method
  • sensor array processing
  • truncated power iteration

ASJC Scopus subject areas

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences


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