奇特征有限域上正交空间生成的压缩感知矩阵
Compressed sensing matrices from orthogonal spaces over finite fields of odd characteristic
AI总结：
本文从奇特征有限域正交空间子空间构造确定性压缩感知矩阵，建立其满足受限等距性质的充分条件，通过与DeVore构造对比说明相关性能权衡。
AI中文摘要：
本文从奇特征有限域上正交空间的子空间构造确定性矩阵，并研究其在压缩感知中的适用性。该构造基于三类子空间间的关联关系，产生具有可显式计算维度与相干性的矩阵族。基于相干性估计，我们建立了此类矩阵满足指定稀疏度水平下受限等距性质的充分条件。我们还与DeVore的确定性构造进行数值对比，以说明测量数、相干性与稀疏恢复保证间的权衡关系。
英文摘要：
In this paper, we construct deterministic matrices from subspaces of orthogonal spaces over finite fields of odd characteristic and investigate their applicability to compressed sensing. The construction is based on incidence relations among three types of subspaces, yielding families of matrices with explicitly computable dimensions and coherence. Using coherence-based estimates, we establish sufficient conditions under which these matrices satisfy the Restricted Isometry Property for prescribed sparsity levels. We also provide numerical comparisons with DeVore's deterministic construction to illustrate the trade-off between the number of measurements, coherence, and sparse recovery guarantees.
