Many interesting problems in fields ranging from telecommunications to computational biology can be formalized in terms of large underdetermined systems of linear equations with additional constraints or regularizers. One of the most studied, the compressed sensing problem, consists in finding the solution with the smallest number of non-zero components of a given system of linear equations ##IMG## [http://ej.iop.org/images/1751-8121/53/18/184001/aab3065ieqn001.gif] for known measurement vector ##IMG## [http://ej.iop.org/images/1751-8121/53/18/184001/aab3065ieqn002.gif] and sensing matrix ##IMG## [http://ej.iop.org/images/1751-8121/53/18/184001/aab3065ieqn003.gif] . Here, we will address the compressed sensing problem within a Bayesian inference framework where the sparsity constraint is remapped into a singular prior distribution (called Spike-and-Slab or Bernoulli–Gauss). A solution to the problem is att...

中文翻译：

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使用期望传播的压缩感测重建

电信，计算生物学等领域中许多有趣的问题都可以根据大型线性方程组的欠定系统（带有附加约束或正则项）来形式化。研究最深入的问题之一是压缩感知问题，它是找到给定线性方程组## IMG ##的非零分量最少的解。[http://ej.iop.org/images/ 1751-8121 / 53/18/184001 / aab3065ieqn001.gif]用于已知的测量向量## IMG ## [http://ej.iop.org/images/1751-8121/53/18/184001/aab3065ieqn002.gif]和感应矩阵## IMG ## [http://ej.iop.org/images/1751-8121/53/18/184001/aab3065ieqn003.gif]。这里，我们将在贝叶斯推理框架内解决压缩感知问题，在该框架中将稀疏约束重新映射为奇异先验分布（称为Spike-and-Slab或Bernoulli-Gauss）。解决这个问题的方法是...