关键词: 压缩感知, 测量矩阵优化, 梯度下降, 自适应步长

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