Empirical Bayes and Full Bayes for Signal Estimation

Abstract

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.

arXiv commentThis work was presented at the Information Theory and Application workshop (ITA), San Diego, CA, Feb. 2014

References in corpus (4)

• Message Passing Algorithms for Compressed Sensing
• Expectation-Maximization Gaussian-Mixture Approximate Message Passing
• Parameterless Optimal Approximate Message Passing
• Information Complexity and Estimation

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