Object reconstitution using pseudo-inverse for ghost imaging

We propose a novel method for object reconstruction of ghost imaging based on Pseudo-Inverse, where the original objects are reconstructed by computing the pseudo-inverse of the matrix constituted by the row vectors of each speckle field. We conduct reconstructions for binary images and gray-scale images. With equal number of measurements, our method presents a satisfying performance on enhancing Peak Signal to Noise Ratio (PSNR) and reducing computing time. Being compared with the other existing methods, its PSNR distinctly exceeds that of the traditional Ghost Imaging (GI) and Differential Ghost Imaging (DGI). In comparison with the Compressive-sensing Ghost Imaging (CGI), the computing time is substantially shortened, and in regard to PSNR our method exceeds CGI on grayscale images and performs as well as CGI visually on binary images. The influence of both the detection noise and the accuracy of measurement matrix on PSNR are also presented.