On the Convergence of Orthogonal/Vector AMP: Long-Memory Message-Passing Strategy
On the Convergence of Orthogonal/Vector AMP: Long-Memory Message-Passing Strategy
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DOI：
10.1109/tit.2022.3194855
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发表时间：
2022-12
影响因子：
2.5
通讯作者：
K. Takeuchi
中科院分区：
文献类型：
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作者：
K. Takeuchi
正交/矢量近似消息传递算法(AMP)是一种用于压缩感知信号重构的有效消息传递算法。本文证明了贝叶斯最优的正交/向量AMP在大系统极限下的收敛性质。证明策略基于一种新的长记忆MP方法：第一步是构造一个保证系统收敛的长记忆MP方法。第二步是通过现有的状态演化框架对LM-MP进行大系统分析。第三步，通过对已有的LM-MP阻尼的一种新的统计解释，证明了贝叶斯最优LM-MP的状态演化递推的收敛性质。最后，将贝叶斯最优的LM-MP的状态演化递推精确地简化为贝叶斯最优的正交/向量AMP的状态演化递推。贝叶斯最优的LM-MP的状态演化递推的收敛意味着贝叶斯最优的正交/向量AMP的状态演化递推的收敛。通过数值模拟，验证了有限尺寸系统中有阻尼型正交/矢量型AMP的状态演化结果和LM-MP的一个反面性。
Orthogonal/vector approximate message-passing (AMP) is a powerful message-passing (MP) algorithm for signal reconstruction in compressed sensing. This paper proves the convergence of Bayes-optimal orthogonal/vector AMP in the large system limit. The proof strategy is based on a novel long-memory (LM) MP approach: A first step is a construction of LM-MP that is guaranteed to converge systematically. A second step is a large-system analysis of LM-MP via an existing framework of state evolution. A third step is to prove the convergence of state evolution recursions for Bayes-optimal LM-MP via a new statistical interpretation of existing LM damping. The last is an exact reduction of the state evolution recursions for Bayes-optimal LM-MP to those for Bayes-optimal orthogonal/vector AMP. The convergence of the state evolution recursions for Bayes-optimal LM-MP implies that for Bayes-optimal orthogonal/vector AMP. Numerical simulations are presented to show the verification of state evolution results for damped orthogonal/vector AMP and a negative aspect of LM-MP in finite-sized systems.