2-D Learned Proximal Gradient Algorithm for Fast Sparse Matrix Recovery
2-D Learned Proximal Gradient Algorithm for Fast Sparse Matrix Recovery
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DOI：
10.1109/tcsii.2020.3024912
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发表时间：
2021-04
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影响因子：
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通讯作者：
Chengzhu Yang;Yuantao Gu;Badong Chen;Hongbing Ma;H. So
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作者：
Chengzhu Yang;Yuantao Gu;Badong Chen;Hongbing Ma;H. So
许多实际问题都可以建模为从二维测量数据中恢复稀疏矩阵，这是信号处理领域的重要课题之一。得益于压缩感知的巨大成功，许多经典的迭代算法可以直接应用或重新发明用于矩阵恢复，尽管它们在计算上是昂贵的。为了缓解这一问题，我们提出了一种名为2D学习邻近梯度算法（2D-LPGA）的神经网络，其目的是快速重建目标矩阵。理论分析表明，当网络参数满足一定条件时，可以线性收敛地重构稀疏信号。此外，数值实验表明所提出的方法优于其他经典的计划。
Many real-world problems can be modeled as sparse matrix recovery from two-dimensional (2D) measurements, which is recognized as one of the most important topics in signal processing community. Benefited from the roaring success of compressed sensing, many classical iterative algorithms can be directly applied or reinvented for matrix recovery, though they are computationally expensive. To alleviate this, we propose a neural network named 2D learned proximal gradient algorithm (2D-LPGA), which aims to quickly reconstruct the target matrix. Theoretical analysis reveals that if the parameters of the network satisfy certain conditions, it can reconstruct the sparse signal with linear convergence rate. Moreover, numerical experiments demonstrate the superiority of the proposed method over other classical schemes.