光学学报, 2012, 32 (2): 0211002, 网络出版: 2011-12-16   

随机间距稀疏三元Toeplitz矩阵相位掩模压缩成像

Phase Mask of Sparse Trinary Toeplitz Matrix with Random Pitch in Compressive Imaging
作者单位
1 安徽大学计算智能与信号处理国家重点实验室, 安徽 合肥 230039
2 合肥师范学院数学系, 安徽 合肥 230069
摘要
压缩成像是一种基于压缩传感(CS)理论的新成像方法,其优点是可以用比传统的Nyquist采样定理所需测量数目少得多的测量值重建原稀疏或可压缩图像。在研究Bernoulli和Toeplitz测量矩阵的基础上,提出一种新的随机间距稀疏三元Toeplitz相位掩模矩阵。实验结果表明,在可压缩双透镜成像系统中,与Bernoulli和BernoulliToeplitz相位掩模矩阵相比,新相位掩模矩阵的成像信噪比与之相当。但是随机独立变元个数和非零元个数显著减少,在数据存储与传输时更具优势,物理上更易实现,甚至重建时间是只有它们的21%~66%。
Abstract
Compressive imaging is a new imaging method based on the compressive sensing theory, which has the advantage of sparse/compressible image reconstruction with far fewer measurements than traditional Nyquist samples. By analyzing the existing Bernoulli and Toeplitz matrix, we propose a novel sparse trinary Toeplitz matrix with random pitch for phase mask. Simulation results show that novel phase mask matrices, comparing with Bernoulli and Bernoulli-Toeplitz phase mask matrices, almost have the same signal-to-noise ratio. But with dramatical reduction of the number of independent random variables and the number of non-zeros entries, the novel matrix is more conducive to data transmission and storage and easy for hardware implementation. Even more, the reconstruction time is only about 21%~66% to that of original matrices.

张成, 沈川, 程鸿, 杨海蓉, 韦穗. 随机间距稀疏三元Toeplitz矩阵相位掩模压缩成像[J]. 光学学报, 2012, 32(2): 0211002. Zhang Cheng, Shen Chuan, Cheng Hong, Yang Hairong, Wei Sui. Phase Mask of Sparse Trinary Toeplitz Matrix with Random Pitch in Compressive Imaging[J]. Acta Optica Sinica, 2012, 32(2): 0211002.

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