随机间距稀疏三元Toeplitz矩阵相位掩模压缩成像

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Bernoulli-Toeplitz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%。

Phase Mask of Sparse Trinary Toeplitz Matrix with Random Pitch in Compressive Imaging

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.