Plug in estimation in high dimensional linear inverse problems a rigorous analysis
Plug in estimation in high dimensional linear inverse problems a rigorous analysis
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DOI：
10.1088/1742-5468/ab321a
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发表时间：
2018-06
期刊：
影响因子：
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通讯作者：
A. Fletcher;S. Rangan;Subrata Sarkar;P. Schniter
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文献类型：
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作者：
A. Fletcher;S. Rangan;Subrata Sarkar;P. Schniter
从噪声线性测量中估算向量通常需要使用先验知识或结构性约束，以进行准确的重建。基于关于这些方法的先验知识考虑插件DeNoising与最近开发的矢量近似消息传递（VAMP）算法相结合，该算法本身是通过期望传播技术得出的。对于高维的右上角不变的随机和Lipschitz denoisers，该方法在图像恢复和参数双线性估计中得到了证明。
Estimating a vector from noisy linear measurements often requires use of prior knowledge or structural constraints on 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 . 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 and Lipschitz denoisers. The method is demonstrated on applications in image recovery and parametric bilinear estimation.