压缩感知重构算法的两步深度展开策略研究

Two-step deep unfolding strategy for compressed sensing reconstruction algorithms

针对压缩感知中重构算法的深度展开问题,提出了一种两步深度展开策略(two-step deep unfolding,TwDU)。已有深度展开重构算法通常依赖前一步估计值估计当前值,TwDU对已有深度展开重构算法增加估计深度,依赖于前两步估计值估计当前展开值。TwDU对已有深度展开算法前两步估计值增加了两个训练权重。训练权重优化利用了信号估计值之间的相关特性,可以随着数据的特性自我学习和调整,所提TwDU策略应用于可学习迭代软阈值算法(learned iterative soft thresholding algorithm,LISTA)、可训练迭代软阈值算法(trainable iterative soft thresholding algorithm,TISTA)、可学习近似消息传递算法(learned approximate message passing,LAMP)等已有深度展开算法。通过在一维和二维稀疏信号的仿真验证,TwDU策略在重构精度和收敛速度上都更具有明显优势。

A two-step deep unfolding(TwDU)strategy is put forward for the deep unfolding of reconstruction al-gorithms in compressed sensing.The existing deep unfolding reconstruction algorithms usually estimate the current value based on the previous one-step estimated value.TwDU increases the estimation depth for the existing deep unfold-ing reconstruction algorithms and estimates the current unfolding value based on the previous two-step estimation value.TwDU increases two training weights for the previous two-step estimation value in the existing deep unfolding recon-struction algorithm.The training weights are self-adaptive,which can learn and adjust following the changes in data characteristics by themselves and optimize and utilize the correlation among the estimated signal values.The proposed TwDU strategy is applied to the existing deep unfolding reconstruction algorithms,such as the learned iterative soft thresholding algorithm,learned approximate message passing algorithm,and trainable iterative soft thresholding al-gorithm.The simulation results in one-dimensional and two-dimensional sparse signals confirm that the TwDU strategy has obvious advantages regarding reconstruction accuracy and convergence speed.