压缩传感
加性高斯白噪声
降噪
计算机科学
消息传递
算法
噪音(视频)
信号重构
白噪声
信号(编程语言)
高斯分布
噪声测量
高斯噪声
信号处理
人工智能
电信
并行计算
物理
图像(数学)
程序设计语言
雷达
量子力学
作者
Christopher A. Metzler,Arian Maleki,Richard G. Baraniuk
标识
DOI:10.1109/tit.2016.2556683
摘要
A denoising algorithm seeks to remove noise, errors, or perturbations from a signal. Extensive research has been devoted to this arena over the last several decades, and as a result, todays denoisers can effectively remove large amounts of additive white Gaussian noise. A compressed sensing (CS) reconstruction algorithm seeks to recover a structured signal acquired using a small number of randomized measurements. Typical CS reconstruction algorithms can be cast as iteratively estimating a signal from a perturbed observation. This paper answers a natural question: How can one effectively employ a generic denoiser in a CS reconstruction algorithm? In response, we develop an extension of the approximate message passing (AMP) framework, called denoising-based AMP (D-AMP), that can integrate a wide class of denoisers within its iterations. We demonstrate that, when used with a high-performance denoiser for natural images, D-AMP offers the state-of-the-art CS recovery performance while operating tens of times faster than competing methods. We explain the exceptional performance of D-AMP by analyzing some of its theoretical features. A key element in D-AMP is the use of an appropriate Onsager correction term in its iterations, which coerces the signal perturbation at each iteration to be very close to the white Gaussian noise that denoisers are typically designed to remove.
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