CUP-VISAR image reconstruction based on low-rank prior and total-variation regularization
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摘要: 针对基于超快压缩成像(CUP)与二维任意反射面速度干涉仪(VISAR)获得的压缩图像重构冲击波二维条纹的问题，提出了一种基于低秩约束和全变分正则化的压缩图像重构算法。该算法利用条纹图像空间结构的相似性以及平滑性，将重构问题转化为核范数最小化和全变分正则化的优化问题，利用即插即用的交替方向乘子法将优化问题分裂为多个子问题求解，实现了CUP-VISAR压缩图像的精准重构。仿真结果表明，在大噪声的条件下，重构图像的峰值信噪比提高了8.45 dB，结构相似性提高了8.52%，重构效果优于主流重构算法。进一步设计实际实验，实验结果表明，冲击波条纹的最大速度相对误差从13.5%降低到3.46%，减少了近10%，验证了算法的有效性。Abstract: To solve the problem of reconstructing two-dimensional shock wave fringe from compressed image obtained from Compressed Ultrafast Photography (CUP) and two-dimensional Velocity Interferometer System for Any Reflector (VISAR), a compressed image reconstruction algorithm based on low-rank constraint and total-variation regularization is proposed. The algorithm uses the similarity and smoothness of the spatial structure of the fringe image to transform the reconstruction problem into an optimization problem of kernel norm minimization and total-variation regularization, and splits the optimization problem into multiple sub-problems using the plug-and-play alternate direction multiplier method to solve the optimization problem, thus realizing accurate reconstruction of the CUP-VISAR compressed image. The simulation results show that under the condition of high noise, the peak signal-to-noise ratio of the reconstructed image is increased by 8.45 dB, and the structural similarity is increased by 8.52%. The reconstruction effect is better than that of the mainstream reconstruction algorithm. The experimental results show that the relative error of the maximum velocity of the shock wave fringe is reduced from 13.5% to 3.46% (reduced by nearly 10%), which verifies the effectiveness of the algorithm.
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