基于稀疏度自适应的压缩感知重构算法研究

Research on compressed sensing reconstruction algorithm based on sparsity adaptation

为了解决在信号和图像重构中前向搜索正交匹配追踪算法需要在稀疏度已知的条件下进行重构,且重构精度不足的问题,提出了一种稀疏度自适应的回溯前向搜索正交匹配追踪算法。在稀疏度未知的情况下,引入了回溯策略来筛选原子,然后通过前向预测策略筛选出残差最小的原子加入支撑集进行迭代,并自适应更新步长,加快了算法收敛速度,提高了信息重构的精度。通过仿真实验发现,与同类算法相比,该算法信号重建噪声比、精确重建率、相对误差性能在一维点目标仿真和二维图像仿真方面均优于同类算法,证实了方法的有效性。

In order to solve the forward search orthogonal matching pursuit algorithm in signal and image reconstruction,it is necessary to reconstruct under the condition of known sparsity.And the reconstruction accuracy is insufficient.In this paper,a sparsity adaptive backtracking forward search orthogonal matching pursuit algorithm is proposed.The algorithm is in the case of unknown sparsity,introduce a backtracking strategy in the atom-screening process.Then the forward prediction strategy is used to select the atom with the smallest residual and add it to the support set for iteration and adaptive update step size.Through these,the convergence speed of the algorithm is accelerated,and the accuracy of information reconstruction is improved.Simulation experiments have found that compared to the same algorithm,the proposed algorithm outperforms the signal reconstruction noise ratio,exact reconstruction rate,and relative error performance in 1-D point target simulation and 2-D image simulation.Therefore,the effectiveness of this method has been verified.