超稀疏三元循环测量矩阵的设计

Super-sparse tri-value circulant measurement matrices design

在伯努利循环矩阵的基础上,对其独立元素中随机地引入零元,形成超稀疏三元循环矩阵,与伯努利-循环矩阵相比,其随机独立变元个数和矩阵非零元数目显著减少,从而有利于信息的传输和存储.数值实验结果表明:提出的测量矩阵重建效果略优于伯努利矩阵和伯努利循环矩阵的重建效果,并在绝大多数情形下重建时间可以降低到原来的10%~40%,加快了后端信号重建的速度,有利于压缩感知理论的实用化.

Zero elements were introduced into Bernoulli circulant matrices to form sparse tri-value cir-culant matrices with non-zeros elements randomly located .In contrast to Bernoulli circulant matrices , the numbers of random independent variables and non-zero elements can be reduced significantly , which is conducive to data transmission and storage .Numerical results show that the reconstructions of sparse tri-value circulant measurement matrices with random pitch are slightly better than Bernoulli and Bernoulli circulant matrices .In most cases ,the reconstruction time is only about 10% ~40% of the reconstruction time of original Bernoulli and Bernoulli circulant matrices ,w hich can greatly accel-erate the speed of the back-end signal reconstruction and is conducive to practical compressed sensing theory .