As compared to using randomly generated sensing matrices, optimizing the sensing matrix w.r.t. a carefully designed criterion is known to lead to better quality signal recovery given a set of compressive measurements. In this paper, we propose generalizations of the well-known mutual coherence criterion for optimizing sensing matrices starting from random initial conditions. We term these generalizations as bi-coherence or tri-coherence and they are based on a criterion that discourages any one column of the sensing matrix from being close to a sparse linear combination of other columns. We also incorporate training data to further improve the sensing matrices through weighted coherence, weighted bi-coherence, or weighted tri-coherence criteria, which assign weights to sensing matrix columns as per their importance. An algorithm is also presented to solve the optimization problems. Finally, the effectiveness of the proposed algorithm is demonstrated through empirical results.

翻译：与使用随机生成的感测矩阵相比,优化经过仔细设计的感测矩阵标准已知能够提高信号恢复质量,因为有一套压缩测量方法。在本文中,我们建议从随机初始条件出发,对众所周知的优化感测矩阵相互一致标准进行概括化,从随机初始条件出发,将这些概括性称为双一致性或三一致性,其依据的标准是,使感测矩阵的任何一栏不接近其他列的稀少线性组合。我们还纳入了培训数据,以便通过加权一致性、加权双一致性或加权三一致性标准进一步改进感测矩阵,根据重要性对感测矩阵列进行加权分量。还介绍了一种算法,以解决优化问题。最后,通过经验结果可以证明拟议的算法的有效性。