REGULARIZATION USING DENOISING: EXACT AND ROBUST SIGNAL RECOVERY

Gavaskar, RG and Chaudhury, KN (2022) REGULARIZATION USING DENOISING: EXACT AND ROBUST SIGNAL RECOVERY. In: 47th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2022, 23 - 27 May 2022, Virtual, Online at Singapore, pp. 5533-5537.

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Abstract

We consider the problem of signal reconstruction from linearly corrupted data using plug-and-play (PnP) regularization. As opposed to traditional sparsity-promoting regularizers, PnP uses an off-the-shelf denoiser within a proximal algorithm such as ISTA or ADMM for image reconstruction. Although PnP has become popular in the imaging community, its regularization capacity is not fully understood. For example, it is not known if PnP can in theory recover a signal from few noiseless measurements as in classical compressed sensing and if the recovery is robust. We explore these questions in this work and present some theoretical and experimental results. In particular, we prove that if the denoiser in question has low rank and if the ground-truth lies in the range of the denoiser, then it can be recovered exactly from noiseless measurements. To the best of knowledge, this is first such result. Furthermore, we show using numerical simulations that even if the aforementioned conditions are violated, PnP recovery is robust in practice. We formulate a theorem regarding the recovery error based on these observations. © 2022 IEEE

Item Type:	Conference Paper
Publication:	ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
Publisher:	Institute of Electrical and Electronics Engineers Inc.
Additional Information:	The copyright for this article belongs to the Institute of Electrical and Electronics Engineers Inc.
Keywords:	compressed sensing; Image regularization; inpainting; plug-and-play; robust recovery
Department/Centre:	Division of Electrical Sciences > Electrical Engineering
Date Deposited:	21 Jun 2022 10:37
Last Modified:	21 Jun 2022 10:37
URI:	https://eprints.iisc.ac.in/id/eprint/73940

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