随机间距稀疏三元循环相位掩膜矩阵可压缩成像

Sparse Trinary Circulant Measurement Matrices with Random Spacing in Compressive Imaging

可压缩成像是一种新兴的基于压缩感知理论的新成像技术,其核心思想是如果空间场景是稀疏或可压缩,那么它可以用远少于经典的Nyquist采样数目的测量值捕获的足够信息重构原场景;构建合适的测量矩阵并易于使用物理实现压缩感知理论中对于图像的随机线性测量是可压缩成像理论实用化的关键之一。该文在研究Bernoulli和Circulant矩阵的基础上,提出一种新的随机间距稀疏三元循环相位掩膜矩阵。模拟实验结果表明,在可压缩双透镜成像系统单次曝光下,与Bernoulli和Bernoulli-Circulant相位掩膜矩阵相比,新相位掩膜矩阵的成像信噪比与之相当;但是该文提出的矩阵随机独立变元个数和非零元个数显著减少,易于数据存储与传输;更重要的是物理上更容易实现,重构时间是只有原来的约20%~50%。新的相位掩膜矩阵的研究对于可压缩成像理论的实际应用具有重要的意义。

Compressive imaging is a novel imaging method based on compressive sensing theory,the key idea is that it can reconstruct original scene precisely with far fewer measurements than Nyquist samples if the scene is sparse/compressible;Constructing an appropriate measurement matrix easy to realize random linear measurement of an image is one of the key points of practical compressive sensing.In this paper,analyzing the existing Bernoulli and Circulant matrices,a novel sparse trinary circulant measurement matrix with random spacing for phase mask is proposed.Simulation results show that novel phase mask matrices,compared to Bernoulli and Ber-noulli-Circulant（BC） phase mask matrices,have the same signal-to-noise ratio;But with the number of inde-pendent random variables and the number of non-zeros entries a dramatically reduction,which is more conducive to data transmission and storage;more importantly that is easy to hardware implementation and the reconstructed time is only about 20%~50% of that of original matrices,which has a significance effects on practical compressive sensing.