Non-convex priors in Bayesian compressed sensing
Non-convex priors in Bayesian compressed sensing
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发表时间：
2009-12
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通讯作者：
S. D. Babacan;L. Mancera;R. Molina;A. Katsaggelos
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作者：
S. D. Babacan;L. Mancera;R. Molina;A. Katsaggelos
我们提出了一种新的贝叶斯公式，用于从压缩测量值进行重建。我们证明了基于lp-范数的高稀疏性执行先验，0 <; p ≤ 1，可以通过优化最小化方法在贝叶斯框架内使用。通过采用一个完整的贝叶斯分析的压缩传感系统和变分贝叶斯分析的推理，所提出的框架提供了模型参数估计沿着的未知信号，以及这些估计的不确定性。我们还表明，一些现有的方法可以推导出所提出的框架的特殊情况。实验结果表明，与常用的压缩感知恢复方法相比，该算法具有较高的性能。
We propose a novel Bayesian formulation for the reconstruction from compressed measurements. We demonstrate that high-sparsity enforcing priors based on lp-norms, with 0 <; p ≤ 1, can be used within a Bayesian framework by majorization-minimization methods. By employing a fully Bayesian analysis of the compressed sensing system and a variational Bayesian analysis for inference, the proposed framework provides model parameter estimates along with the unknown signal, as well as the uncertainties of these estimates. We also show that some existing methods can be derived as special cases of the proposed framework. Experimental results demonstrate the high performance of the proposed algorithm in comparison with commonly used methods for compressed sensing recovery.