Bilinear Recovery Using Adaptive Vector-AMP

Subrata Sarkar, Alyson K. Fletcher, Sundeep Rangan, Philip Schniter

Research output: Contribution to journalArticlepeer-review


We consider the problem of jointly recovering the vector b and the matrix C from noisy measurements Y = A(b)C + W, where A(·) is a known affine linear function of b(i.e., A(b)=A0 + ∑i=1Q biAi with known matrices Ai). This problem has applications in matrix completion, robust PCA, dictionary learning, self-calibration, blind deconvolution, joint-channel/symbol estimation, compressive sensing with matrix uncertainty, and many other tasks. To solve this bilinear recovery problem, we propose the Bilinear Adaptive Vector Approximate Message Passing (VAMP) algorithm. We demonstrate numerically that the proposed approach is competitive with other state-of-the-art approaches to bilinear recovery, including lifted VAMP and Bilinear Generalized Approximate Message Passing.

Original languageEnglish (US)
Article number8712432
Pages (from-to)3383-3396
Number of pages14
JournalIEEE Transactions on Signal Processing
Issue number13
StatePublished - Jul 1 2019


  • Approximate message passing
  • computed tomography
  • dictionary learning
  • expectation maximization
  • expectation propagation
  • self-calibration

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering


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