Convolutional Approximate Message-Passing
Convolutional Approximate Message-Passing
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DOI：
10.1109/lsp.2020.2976155
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发表时间：
2020-01-01
影响因子：
3.9
通讯作者：
Takeuchi, Keigo
中科院分区：
文献类型：
--
作者：
Takeuchi, Keigo
提出了一种新的用于压缩感知信号恢复的消息传递算法。该算法克服了近似消息传递(AMP)算法和正交/矢量AMP算法的缺点，实现了各自的优点。AMP只收敛于有限的一类感知矩阵，且复杂度较低。正交/向量AMP算法对矩阵求逆的复杂度要求很高，但它适用于多种类型的感知矩阵。该算法的关键特征是通过对所有先前迭代中的消息进行卷积来实现所谓的Onsager校正，而传统的消息传递算法具有仅依赖于最近一次迭代中的消息的校正项。因此，所提出的算法称为卷积AMP(CAMP)。以不能保证AMP收敛的病态感知矩阵为例进行了仿真。数值模拟结果表明，虽然AMP的复杂度比AMP低，但CAMP能改善AMP的收敛性能，并获得与正交/矢量AMP相当的高性能。
This letter proposes a novel message-passing algorithm for signal recovery in compressed sensing. The proposed algorithm solves the disadvantages of approximate message-passing (AMP) and orthogonal/vector AMP, and realizes their advantages. AMP converges only in a limited class of sensing matrices while it has low complexity. Orthogonal/vector AMP requires a high-complexity matrix inversion while it is applicable for a wide class of sensing matrices. The key feature of the proposed algorithm is the so-called Onsager correction via a convolution of messages in all preceding iterations while the conventional message-passing algorithms have correction terms that depend only on messages in the latest iteration. Thus, the proposed algorithm is called convolutional AMP (CAMP). Ill-conditioned sensing matrices are simulated as an example in which the convergence of AMP is not guaranteed. Numerical simulations show that CAMP can improve the convergence property of AMP and achieve high performance comparable to orthogonal/vector AMP in spite of low complexity comparable to AMP.