TY - JOUR
T1 - Plug-in estimation in high-dimensional linear inverse problems
T2 - 32nd Conference on Neural Information Processing Systems, NeurIPS 2018
AU - Fletcher, Alyson K.
AU - Pandit, Parthe
AU - Rangan, Sundeep
AU - Sarkar, Subrata
AU - Schniter, Philip
N1 - Funding Information:
A. K. Fletcher and P. Pandit were supported in part by the National Science Foundation under Grants 1738285 and 1738286 and the Office of Naval Research under Grant N00014-15-1-2677. S. Rangan was supported in part by the National Science Foundation under Grants 1116589, 1302336, and 1547332, and the industrial affiliates of NYU WIRELESS. The work of P. Schniter was supported in part by the National Science Foundation under Grant CCF-1527162.
Publisher Copyright:
© 2018 Curran Associates Inc.All rights reserved.
PY - 2018
Y1 - 2018
N2 - 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.
AB - 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.
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M3 - Conference article
AN - SCOPUS:85062725996
SN - 1049-5258
VL - 2018-December
SP - 7440
EP - 7449
JO - Advances in Neural Information Processing Systems
JF - Advances in Neural Information Processing Systems
Y2 - 2 December 2018 through 8 December 2018
ER -