论文标题
用于压缩感应的准正交匹配追踪算法
A Quasi-Orthogonal Matching Pursuit Algorithm for Compressive Sensing
论文作者
论文摘要
在本文中，我们提出了一种称为QuASI-OMP算法的新的正交匹配追求算法，该算法极大地增强了经典的正交匹配追踪（OMP）算法的性能，并以计算复杂性为代价。我们能够证明，在传感矩阵的相互连贯性的一些足够条件下，QOMP算法成功地在噪声和嘈杂和嘈杂的设置下选择了2S列的S-Sparse信号矢量X恢复了S-Sparse信号矢量X。此外，我们表明，对于高斯传感矩阵，每次迭代的残差的范数将零线性地取决于矩阵的大小，概率很高。证明了数值实验可以显示QOMP算法在恢复稀疏溶液中的有效性，从而胜过经典的OMP和GOMP算法。
In this paper, we propose a new orthogonal matching pursuit algorithm called quasi-OMP algorithm which greatly enhances the performance of classical orthogonal matching pursuit (OMP) algorithm, at some cost of computational complexity. We are able to show that under some sufficient conditions of mutual coherence of the sensing matrix, the QOMP Algorithm succeeds in recovering the s-sparse signal vector x within s iterations where a total number of 2s columns are selected under the both noiseless and noisy settings. In addition, we show that for Gaussian sensing matrix, the norm of the residual of each iteration will go to zero linearly depends on the size of the matrix with high probability. The numerical experiments are demonstrated to show the effectiveness of QOMP algorithm in recovering sparse solutions which outperforms the classic OMP and GOMP algorithm.
