中文摘要：

压缩数据分离是信号采样理论的研究热点之一.本文给出了在冗余字典满足相互一致性条件和完全扰动矩阵满足限制性同构条件下,非凸lq（0〈q≤1）极小化的压缩数据分离问题的重构条件和误差估计，理论结果表明在不同冗余字典和不同扰动下，此方法仍能鲁棒重构原始信号．基于两种不同的冗余字典一离散余弦变换（DCT）和小波变换（WT），我们执行了一系列仿真实验，验证了在测量矩阵受各种扰动和加性噪音下，非凸lq（0〈q≤1）极小化方法具有较强的鲁棒性和稳定性．本文结果为压缩感知和数据分离的进一步发展和应用提供借鉴．

英文摘要：

Compressed data separation is one of the hot research theories of signal sampling. Under the condition that the redundant dictionary and perturbation matrix satisfy mutual coherence and restricted isometry property,respectively,the reconstruction condition and error estimation of compressed data separation via nonconvex lq（ 0 〈q≤1） minimization are established. Under different redundant dictionaries and perturbation,our results showthat nonconvex lq（ 0〈 q≤1） minimization can still robustly reconstruct the original signal. In viewof two different redundant dictionaries—the discrete cosine transform and wavelet transform,we conduct a series of simulation experiments to testify the strong robustness and stability of nonconvex lq（ 0 q≤1） minimization method with various perturbation and additive noise. The obtained results provide a reference for further development and application of compressed sensing and data separation.