论文标题
贝叶斯最佳卷积放大器
Bayes-Optimal Convolutional AMP
论文作者
论文摘要
本文提出了贝叶斯最佳卷积近似消息通话（CAMP），用于压缩感测信号回收。 CAMP使用相同的低复杂性匹配的过滤器（MF）进行干扰抑制与近似消息通话（AMP）。为了提高AMP的收敛性对于不良条件的传感矩阵，所谓的Amp中的Onsager校正项被所有先前消息的卷积所取代。确定卷积中的TAP系数，以便在正交不变的传感矩阵的假设下通过状态进化（SE）实现估计误差的渐近高斯性。得出一个SE方程以优化cAMP中的Dinoisers的序列。如果SE等式收敛到固定点，并且固定点是唯一的，则优化的营地被证明是所有正交传感矩阵的贝叶斯最佳选择。对于具有低到中度状况数量的传感矩阵，CAMP可以实现与需要线性最小均值误差（LMMSE）滤波器而不是MF的高复杂性正交/向量放大器相同的性能。
This paper proposes Bayes-optimal convolutional approximate message-passing (CAMP) for signal recovery in compressed sensing. CAMP uses the same low-complexity matched filter (MF) for interference suppression as approximate message-passing (AMP). To improve the convergence property of AMP for ill-conditioned sensing matrices, the so-called Onsager correction term in AMP is replaced by a convolution of all preceding messages. The tap coefficients in the convolution are determined so as to realize asymptotic Gaussianity of estimation errors via state evolution (SE) under the assumption of orthogonally invariant sensing matrices. An SE equation is derived to optimize the sequence of denoisers in CAMP. The optimized CAMP is proved to be Bayes-optimal for all orthogonally invariant sensing matrices if the SE equation converges to a fixed-point and if the fixed-point is unique. For sensing matrices with low-to-moderate condition numbers, CAMP can achieve the same performance as high-complexity orthogonal/vector AMP that requires the linear minimum mean-square error (LMMSE) filter instead of the MF.
