一种基于单像素相机的压缩感知图像重建优化算法

An Optimization Algorithm for Compressed Sensing Image Reconstruction Based on Single Pixel Camera

摘要:

基于压缩感知图像重构和单像素相机成像的基本原理,对单像素成像系统中的图像重建算法进行了改进优化。基于最小范数类优化算法,结合凸优化算法和非凸优化算法各自的优点,设计了一种逼近L₀范数的数学模型,从而实现了从凸优化向非凸优化算法的迭代逼近,即逼近光滑L₀范数算法。该新型算法以更高的效率和更大的概率逼近原始信号全局最优且尽可能稀疏的解。相较于传统压缩感知图像重建的贪婪类算法和最小范数类算法,该算法使压缩感知重建图像的质量和单像素相机的成像效果均得到了有效提升,并通过实验仿真和实际场景的成像实验验证了该优化算法的可行性。

Abstract:

Based on the basic principles of single-pixel camera imaging and compressed sensing image reconstruction, the image reconstruction algorithm of single-pixel camera was optimized. Based on the optimization algorithm of minimum norm and by combining the advantages of convex optimization and non-convex optimization, a mathematical model approximating L₀ norm was designed to realize the iterative approximation from convex optimization to non-convex optimization, and a new algorithm approximating the smooth L₀ norm algorithm was proposed. The proposed algorithm approximates the global optimal solution as sparse as possible with higher efficiency and greater probability. Compared with the traditional greedy algorithm and minimum norm algorithm, the new algorithm improves the quality of reconstructed images and imaging effectively, and its feasibility was verified by simulations and actual single-pixel imaging experiments.