采用迭代投影方法的测量矩阵训练算法

The Measurement Matrix Training Algorithm Using Iteration Projection Method

针对稀疏重建过程中感知矩阵的约束等距性质或累积增量难以满足约束条件,即具有较小的RIP常数或者累积增量这一问题,文中在给定变换矩阵条件下,提出了一种基于迭代投影方法训练测量矩阵的算法,从而使得感知矩阵的累积增量逼近了1/2这一约束界。实验表明,该算法训练出的测量矩阵与训练前相比,其感知矩阵累积增量大大降低,且明显提高了正交匹配追踪算法重建稀疏信号的成功率。

The sensing matrix with a minor RIP constant or cumulative coherence cannot be easily sufficed in the progress of sparse reconstruction. This article proposed a novel measurement matrix training algo- rithm based on iterative projection method for a deterministic transformation matrix. The algorithm makes the cumulative coherence of the sensing matrix approximate to the constraint boundary 1/2. Experiments show that the cumulative coherence of the obtained sensing matrix is reduced via the new algorithm. And the sensing matrix improves recovery rate of OMP algorithm compared with training before.