Compressed Imaging Reconstruction with Sparse Random Projection

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.