Performance Analysis of Approximate Message Passing for Distributed Compressed Sensing
Performance Analysis of Approximate Message Passing for Distributed Compressed Sensing
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DOI：
10.1109/jstsp.2018.2850754
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发表时间：
2017-12
影响因子：
7.5
通讯作者：
Gabor Hannak;A. Perelli;Norbert Goertz;Gerald Matz;Mike E. Davies
中科院分区：
文献类型：
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作者：
Gabor Hannak;A. Perelli;Norbert Goertz;Gerald Matz;Mike E. Davies
贝叶斯近似消息传递（BAMP）是一种有效的压缩感知方法，在最小均方误差（MMSE）意义上几乎是最优的。多测量向量(MMV)-BAMP对具有相同支持度的多个向量进行联合恢复，并考虑感兴趣信号和噪声之间的相关性。在本文中，我们展示了如何通过信号和噪声向量的简单联合去相关（对角化）变换来降低向量BAMP的复杂性，这也便于后续的性能分析。我们证明了相应的状态演化相对于联合去相关变换是等变的，并且保持了伯努利-高斯先验的残差噪声协方差的对角性。我们利用这些结果通过复制方法分析BAMP的动力学和均方误差（MSE）性能，从而了解信号相关性和联合稀疏信号数量的影响。最后，我们评估了MMV-BAMP在具有相关颜色通道的单像素成像中的应用，从而探讨了与传统BAMP重建和组套索相比，关节恢复的性能增益。
Bayesian approximate message passing (BAMP) is an efficient method in compressed sensing that is nearly optimal in the minimum mean squared error (MMSE) sense. Multiple measurement vector (MMV)-BAMP performs joint recovery of multiple vectors with identical support and accounts for correlations in the signal of interest and in the noise. In this paper, we show how to reduce the complexity of vector BAMP via a simple joint decorrelation (diagonalization) transform of the signal and noise vectors, which also facilitates the subsequent performance analysis. We prove that the corresponding state evolution is equivariant with respect to the joint decorrelation transform and preserves diagonality of the residual noise covariance for the Bernoulli–Gauss prior. We use these results to analyze the dynamics and the mean squared error (MSE) performance of BAMP via the replica method, and thereby understand the impact of signal correlation and number of jointly sparse signals. Finally, we evaluate an application of MMV-BAMP for single-pixel imaging with correlated color channels and thereby explore the performance gain of joint recovery compared to conventional BAMP reconstruction as well as group lasso.