Signal Recovery from Inconsistent Nonlinear Observations

We show that many nonlinear observation models in signal recovery can be represented using firmly nonexpansive operators. To address problems with inaccurate measurements, we propose solving a variational inequality relaxation which is guaranteed to possess solutions under mild conditions and which...

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Bibliographic Details
Main Authors: Combettes, Patrick L., Woodstock, Zev C.
Format: Conference Proceeding
Language:English
Subjects:
Acoustics
Conferences
Firmly nonexpansive operator
inconsistent nonlinear observations
Signal processing
Signal processing algorithms
signal recovery
Speech processing
variational inequality
Online Access:Request full text
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Summary:We show that many nonlinear observation models in signal recovery can be represented using firmly nonexpansive operators. To address problems with inaccurate measurements, we propose solving a variational inequality relaxation which is guaranteed to possess solutions under mild conditions and which coincides with the original problem if it happens to be consistent. We then present an efficient algorithm for its solution, as well as numerical applications in signal and image recovery, including an experimental operator-theoretic method of promoting sparsity.
ISSN:2379-190X
DOI:10.1109/ICASSP43922.2022.9746145