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
图像处理 压缩传感 压缩成像 确定性测量 稀疏三元Toeplitz矩阵 相位掩模矩阵 image processing compressive sensing compressive imaging deterministic measurement sparse trinary Toeplitz matrix phase mask matrix
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.