内投影神经网络对l1-αl2极小化问题的稀疏信号恢复
An Inertial Projection Neural Network for Sparse Signal Recovery via l1-αl2Minimization
摘要: 本文旨在开发一种新算法，从少量测量数据中恢复稀疏信号，这是压缩传感领域的一个基本问题。目前，压缩感知倾向于非相干系统，其中任何两个测量值的相关性都尽可能小。然而，在现实中，许多问题是相干的，传统的方法，如l1最小化，处理效果不佳。我们提出了一种新的基于惯性投影神经网络的压缩传感l1-αl2极小化问题。针对高相干测量矩阵的稀疏信号恢复，提出了l1极小化问题，不同于传统的使用标准凸松弛的l1-αl2极小化问题。本文详细介绍了如何将惯性投影神经网络应用到压缩传感技术中。此外，还进行了数值实验，证明了稀疏信号恢复算法的有效性和显著的性能。
Abstract: This paper aims to develop a new algorithm for recovering a sparse vector from a small number of measurements, which is a fundamental problem in the field of compressive sensing (CS). Currently, CS favors incoherent systems, in which any two measurements are as little correlated as possible. In reality, however, many problems are coherent, conventional methods such as l1 minimization, do not work well. We propose a l1-αl2 minimization problem for compressed sensing using inertial projection neural network. The l1-αl2 minimization problem is presented for sparse signal recovery from highly coherent measurement matrices, differing from conventional l1 mini-mization which uses standard convex relaxation. We describe in details how to incorporate inertial projection neural network into compressed sensing. Furthermore, numerical experiments are conducted to support the effectiveness and remarkable performance of the algorithm for sparse signal recovery.
文章引用：罗晓敏. 内投影神经网络对l1-αl2极小化问题的稀疏信号恢复[J]. 应用数学进展, 2019, 8(2): 301-308. https://doi.org/10.12677/AAM.2019.82034

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