Iterative deconvolution methods for ghost imaging

Abstract

Ghost imaging (GI) is an important technique in single-pixel imaging. It has been demonstrated that GI has applications in various areas such as imaging through harsh environments and optical encryption. Correlation is widely used to reconstruct the object image in GI. But it only offers the signal-to-noise ratios (SNR) of the reconstructed image linearly proportional to the number of measurements. Here, we develop a kind of iterative deconvolution methods for GI. With the known image transmission matrix in GI, the first one uses an iterative algorithm to decrease the error between the reconstructed image and the ground-truth image. Ideally, the error converges to a minimum for speckle patterns when the number of measurements is larger than the number of resolution cells. The second technique, Gerchberg-Saxton (GS) like GI, takes the advantage of the integral property of the Fourier transform, and treats the captured data as constraints for image reconstruction. According to this property, we can regard the data recorded by the bucket detector as the Fourier transform of the object image evaluated at the origin. Each of the speckle patterns randomly selects certain spectral components of the object and shift them to the origin in the Fourier space. One can use these constraints to reconstruct the image with the GS algorithm. This deconvolution method is suitable for any single pixel imaging models. Compared to conventional GI, both techniques offer a nonlinear growth of the SNR value with respect to the number of measurements.