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Plug-in Estimation in High-Dimensional Linear Inverse Problems: A Rigorous Analysis
Alyson Fletcher · Parthe Pandit · Sundeep Rangan · Subrata Sarkar · Philip Schniter

Wed Dec 05 07:45 AM -- 09:45 AM (PST) @ Room 210 #61
Estimating a vector $\mathbf{x}$ from noisy linear measurements $\mathbf{Ax+w}$ often requires use of prior knowledge or structural constraints on $\mathbf{x}$ 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 $\mathbf{x}$. 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-in" VAMP can be exactly predicted for a large class of high-dimensional random $\Abf$ and denoisers. The method is illustrated in image reconstruction and parametric bilinear estimation.

Author Information

Alyson Fletcher (UCLA)
Parthe Pandit (UCLA)
Sundeep Rangan (NYU)
Subrata Sarkar (The Ohio State University)
Philip Schniter (The Ohio State University)

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