图像重建中的非常稀疏循环矩阵

Very sparse circulant matrices in image reconstruction

测量矩阵是压缩传感理论的关键要素之一。针对目前大部分工作中所用的高斯等随机测量矩阵独立随机变元过多,不利于物理实现的问题,引入稀疏带状和稀疏列的概念,形成稀疏带状随机、托普利兹和循环矩阵以及稀疏列随机、循环矩阵,随机变元个数减少约三分之一。采用通用的模拟实验方法,验证此类稀疏矩阵对于真实图像的重建效果及对0-1信号的成功重建概率均与随机高斯矩阵相当。

Measurement matrix is one of the key components in compressed sensing. Most work so far focuses on Gaussian or Bernoulli random measurements. However, such matrices are often diffcnlt and costly to implement in hardware realizations because of too many independent random variables. This paper introduces sparse banded and column measurements matrix for reconstructing signals that independent random variables are reduced more than one-third. Simulation experiments show that the reconstruction effect of true image and the probability of 0-1 signal of the sparse matrix are the same as those of random Gaussian matrix.