中文摘要：

众所周知,传统的信号压缩和重建遵循香农一耐奎斯特采样定律,即采样率必须至少为信号最高频率的两倍,才能保证在重建时不产生失真,这无疑将给信号采样,传输和存储过程带来越来越大的压力.随着科技的飞速发展,特别是近年来传感器技术获取数据能力提高,物联网等促使人类社会的数据规模遽增,大数据时代正式到来.大数据的规模效应给数据存储,传输,管理以及数据分析带来了极大的挑战.压缩采样应运而生.限制等距性（Restricted Isometry Property,RIP）在压缩传感中起着关键的作用.只有满足限制等距条件的压缩矩阵才能平稳恢复原始信号.RIP作为衡量矩阵是否能作为测量矩阵得到了认可,但是此理论的缺陷在于对任一矩阵,很难有通用,快速的算法来验证其是否满足RIP条件.很多学者尝试弱化RIP条件以找到测量矩阵构造的突破口.首先构造了新的限制等距条件δ（1.5k）＋θ（k,1.5k）≤1,然后证明在这个条件下无噪声稀疏信号能被精确的恢复,并且噪声稀疏信号能被平稳的估计.最后,通过比较表明δ（1.5k）＋θ（k,1.5k）≤1优于现存的条件.

英文摘要：

As we all know,the traditional signal compression and reconstruction follow the Shannon-Nyquist sampling theorem.The sampling rate must be at least twice the highest frequency signal,in order to ensure that reconstruction does not produce distortion.It undoubtedly is hard to sample transport and storage.With the rapid development of technology,especially in recent years sensor technology of obtaining data capacity improving,the size of data on networking dramatic Increase.the official arrival of the era of big data.Large scale data storage,transmission,management,and analysis has brought great challenges.Compressed samples emerged.Restricted Isometry Property plays a key role in the compressed sensing.Only meeting RIP conditions matrix can smoothly recover the original signal.But the drawback of this theory is that for a given matrix,it is very difficult to verify its meeting this condition.Many scholars try to find a breakthrough on conditions of weaken RIP measurement matrix structure.Firstly,construct new restrictions isometric conditions,then we can prove stable recovering of high-dimensional sparse signals both in the noiseless case and noisy case under this condition.Finally,the results indicate the presented condition weaker the condition of some existing results.