Abstract: In compressed sensing, the recostruction accuracy can be improved by reducing the column coherence of the sensing matrix. Because sparse dictionaries are generally fixed, the coherence of the sensing matrix is now primarily reduced by optimizing the measurement matrix. An improved measurement matrix optimization algorithm is proposed. The gradient descent method is used to update the measurement matrix. Combining the Barzilai-Borwen method and the Armijo criterion, the step size can be adjusted adaptively in the iteration and guarantee the convergence of the algorithm. The simulation results show that the proposed method has faster convergence speed and can obtain better measurement matrix.

Key words: compressed sensing, measurement matrix optimization, gradient descent, adaptive step-size

摘要： 在压缩感知中，降低传感矩阵的列相干性可以提高重构精度。因为稀疏字典一般是固定的，所以目前主要通过优化测量矩阵来间接降低传感矩阵列相干性。提出一种改进的测量矩阵优化算法，使用梯度下降法更新测量矩阵并结合Barzilai-Borwen方法以及Armijo准则，使步长能够在迭代中自适应调整并保证算法收敛性。仿真实验表明，所提出的方法具有更快的收敛速度并且能够得到更优的测量矩阵。

关键词: 压缩感知, 测量矩阵优化, 梯度下降, 自适应步长