确定性矩阵可分离压缩成像

张成; 程鸿; 张芬; 韦穗

doi:doi:10.3788/gzxb20154403.0311003

光子学报, 2015, 44 (3): 0311003, 网络出版: 2015-04-14

确定性矩阵可分离压缩成像

Separable Compressive Imaging with Deterministic Matrices

论文大纲

张成 ^*程鸿张芬韦穗

作者单位

安徽大学计算智能与信号处理教育部重点实验室, 安徽省现代成像与显示技术重点实验室, 合肥 230039

摘要

针对可分离压缩传感使用的可分离随机正交矩阵在处理大尺度图像等高维信号感知时难度太大或成本过高的问题, 引入确定性测量矩阵, 提出确定性矩阵可分离压缩传感, 可将如托普利兹矩阵及循环矩阵等具有确定性结构的矩阵作为可分离压缩传感的左、右可分离矩阵.该方案可以降低独立元素的数目, 从而显著降低前端物理实现的难度与成本.数值模拟实验分别评估了该方法在不同采样率及不同图像尺寸下的压缩重建性能, 结果表明该方法在独立元素非常少的情形下得到与原随机正交矩阵相近的重建质量, 证明了其可行性.

Abstract

Aiming at the heavy difficulty or high cost for the random orthogonal matrix which used in separable compressive sensing for high-dimensional signals sensing, such as large-scale image compressive reconstruction, deterministic measurement matrices was introduced, and a separable compressive sensing using deterministic matrices was proposed, matrix with deterministic structure, such as Toeplitz or Circulant matrix, could be used as a left/right separable matrix in separable compressed sensing. The proposed scheme can significantly reduce the number of independent elements, thus significantly reduce the difficulty and the cost of physical implementation. Numerical simulations evaluated comparisons of reconstruction performance of the proposed method with different downsampling rates and different image sizes. The results indicate that the proposed method can achieve similar reconstruction quality with far fewer independent elements as random orthogonal matrix′s, which demonstrates the feasibility of the proposed method.

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张成, 程鸿, 张芬, 韦穗. 确定性矩阵可分离压缩成像[J]. 光子学报, 2015, 44(3): 0311003. ZHANG Cheng, CHENG Hong, ZHANG Fen, WEI Sui. Separable Compressive Imaging with Deterministic Matrices[J]. ACTA PHOTONICA SINICA, 2015, 44(3): 0311003.

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