Distribution agnostic Bayesian matching pursuit based on the exponential embedded family
Distribution agnostic Bayesian matching pursuit based on the exponential embedded family
复制标题
基于指数嵌入族的分布不可知贝叶斯匹配追踪
DOI：
10.1016/j.neucom.2020.06.007
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发表时间：
2020-10
期刊：
影响因子：
6
通讯作者：
Songcan Chen
中科院分区：
文献类型：
--
作者：
Di Ma;Songcan Chen
压缩感知(CS)是一个新兴的领域，它可以从几个压缩测量中恢复高维稀疏信号。使用贝叶斯框架的经典CS算法通常对信号施加稀疏性提升先验，这可能不能刻画真实信号的分集。此外，估计先前所涉及的参数是具有挑战性的，特别是对于非身份识别的人。信号。在本文中，我们提出了一种有效的先验不可知的贝叶斯匹配追踪法用于稀疏信号恢复，它避免了对信号施加不匹配先验的风险，并且由于消除了先验参数估计，具有比贝叶斯方法更低的复杂度。具体地，我们利用噪声模型和简化的指数嵌入族(EEF)来获得感兴趣的近似似然，然后以贪婪的方式找到近似似然最大的最优支撑点，从而给出稀疏信号的近似最小均方误差(MMSE)估计。实验结果表明，与现有方法相比，该方法具有更低的归一化均方误差(NMSE)和更高的效率。
Compressed sensing (CS) is an emerging field that allows to recover high-dimensional sparse signal from a few compressed measurements. Classical CS algorithms using the Bayesian framework generally impose a sparseness-promoting prior on the signal, which may not characterize the real signals with diversity. Moreover, estimating the parameters involved in the prior is challenging especially for non-i.i.d. signals. In this paper, we propose an efficient prior-agnostic Bayesian matching pursuit for sparse signal recovery, which avoids the risk of imposing mismatched prior on the signals and enjoys lower complexity than Bayesian approaches due to the elimination of prior parameter estimation. Specifically, we utilize the noise model and the reduced exponential embedded family (EEF) to obtain an approximate likelihood of interest, and then find the most dominant supports with maximum approximate likelihoods in a greedy manner to give an approximate minimum mean squared error (MMSE) estimate for the sparse signal. Experiment results demonstrate that our method achieves lower normalized mean squared error (NMSE) while higher efficiency compared to the state-of-the-art methods.
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