Plug-in estimation in high-dimensional linear inverse problems: A rigorous analysis

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

Research output: Contribution to journalConference article

Abstract

Estimating a vector x from noisy linear measurements Ax + w often requires use of prior knowledge or structural constraints on x for accurate reconstruction. Several recent works have considered combining linear least-squares estimation with a generic or “plug-in” denoiser function that can be designed in a modular manner based on the prior knowledge about x. While these methods have shown excellent performance, it has been difficult to obtain rigorous performance guarantees. This work considers plug-in denoising combined with the recently-developed Vector Approximate Message Passing (VAMP) algorithm, which is itself derived via Expectation Propagation techniques. It shown that the mean squared error of this “plug-and-play" VAMP can be exactly predicted for high-dimensional right-rotationally invariant random A and Lipschitz denoisers. The method is demonstrated on applications in image recovery and parametric bilinear estimation.

Original languageEnglish (US)
Pages (from-to)7440-7449
Number of pages10
JournalAdvances in Neural Information Processing Systems
Volume2018-December
StatePublished - Jan 1 2018
Event32nd Conference on Neural Information Processing Systems, NeurIPS 2018 - Montreal, Canada
Duration: Dec 2 2018Dec 8 2018

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ASJC Scopus subject areas

  • Computer Networks and Communications
  • Information Systems
  • Signal Processing

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