As the Internet of Things thrives, monitors and cameras produce tons of image data every day. To efficiently process these images, many compressed imaging frameworks are proposed. A compressed imaging framework comprises two parts, image signal measurement and reconstruction. Although a plethora of measurement devices have been designed, the development of the reconstruction is relatively lagging behind. Nowadays, most of existing reconstruction algorithms in compressed imaging are optimization problem solvers based on specific priors. The computation burdens of these optimization algorithms are enormous and the solutions are usually local optimums. Meanwhile, it is inconvenient to deploy these algorithms on cloud, which hinders the popularization of compressed imaging. In this article, we dive deep into the random projection to build reconstruction algorithms for compressed imaging. We first fully utilize the information in the measurement procedure and propose a combinatorial sparse random projection (SRP) reconstruction algorithm. Then, we generalize the SRP to a novel distributed algorithm called Cloud-SRP (CSRP), which enables efficient reconstruction on cloud. Moreover, we explore the combination of SRP with conventional optimization reconstruction algorithms and propose the Iterative-SRP (ISRP), which converges to a guaranteed fixed point. With minor modifications on the naive optimization algorithms, the ISRP yields better reconstructions. Experiments on real ghost imaging reconstruction reveal that our algorithms are effective. And simulation experiments show their advantages over the classical algorithms.

中文翻译：

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稀疏随机投影的压缩图像重建

随着物联网的蓬勃发展，监视器和摄像头每天都会产生大量的图像数据。为了有效地处理这些图像，提出了许多压缩成像框架。压缩成像框架包括两部分，图像信号测量和重建。尽管已经设计了过多的测量设备，但重建的发展相对滞后。目前，压缩成像中现有的大多数重建算法都是基于特定先验的优化问题求解器。这些优化算法的计算负担是巨大的，并且解决方案通常是局部最优的。同时，这些算法在云端部署不方便，阻碍了压缩成像的普及。在本文中，我们深入研究随机投影来构建压缩成像的重建算法。我们首先充分利用测量过程中的信息，并提出组合稀疏随机投影（SRP）重建算法。然后，我们将 SRP 推广到一种称为 Cloud-SRP (CSRP) 的新型分布式算法，该算法能够在云上进行高效重建。此外，我们探索了 SRP 与传统优化重建算法的结合，并提出了迭代 SRP (ISRP)，它收敛到一个有保证的不动点。通过对朴素优化算法的微小修改，ISRP 产生了更好的重建。真实鬼成像重建实验表明我们的算法是有效的。仿真实验显示了它们相对于经典算法的优势。