Total Least Squares Phase Retrieval

Sidharth Gupta, Ivan Dokmanic

Research output: Contribution to journalArticlepeer-review


We address the phase retrieval problem with errors in the sensing vectors. A number of recent methods for phase retrieval are based on least squares (LS) formulations which assume errors in the quadratic measurements. We extend this approach to handle errors in the sensing vectors by adopting the total least squares (TLS) framework that is used in linear inverse problems with operator errors. We show how gradient descent and the specific geometry of the phase retrieval problem can be used to obtain a simple and efficient TLS solution. Additionally, we derive the gradients of the TLS and LS solutions with respect to the sensing vectors and measurements which enables us to calculate the solution errors. By analyzing these error expressions we determine conditions under which each method should outperform the other. We run simulations to demonstrate that our method can lead to more accurate solutions. We further demonstrate the effectiveness of our approach by performing phase retrieval experiments on real optical hardware which naturally contains both sensing vector and measurement errors.

Original languageEnglish (US)
Pages (from-to)536-549
Number of pages14
JournalIEEE Transactions on Signal Processing
StatePublished - 2022
Externally publishedYes


  • Phase retrieval
  • operator error
  • quadratic equations
  • sensing vector error
  • total least squares

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering


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