信号估计的经验贝叶斯和全贝叶斯方法
Empirical Bayes and Full Bayes for Signal Estimation
摘要：
我们考虑遵循参数分布的信号，其中参数值是未知的。为了从标量信道中的噪声测量中估计这样的信号，我们研究了经验贝叶斯（EB）方法和全贝叶斯（FB）方法的经验性能。然后，我们应用EB和FB解决压缩感知（CS）信号估计问题，通过连续去噪的标量高斯信道内的近似消息传递（AMP）的框架。我们的数值结果表明，FB实现更好的性能比EB在标量信道去噪问题时，信号维数较小时。在CS设置中，信号尺寸必须足够大，AMP才能正常工作;对于大信号尺寸，AMP的性能与FB和EB相似。
英文摘要：
We consider signals that follow a parametric distribution where the parameter values are unknown. To estimate such signals from noisy measurements in scalar channels, we study the empirical performance of an empirical Bayes (EB) approach and a full Bayes (FB) approach. We then apply EB and FB to solve compressed sensing (CS) signal estimation problems by successively denoising a scalar Gaussian channel within an approximate message passing (AMP) framework. Our numerical results show that FB achieves better performance than EB in scalar channel denoising problems when the signal dimension is small. In the CS setting, the signal dimension must be large enough for AMP to work well; for large signal dimensions, AMP has similar performance with FB and EB.
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