Exponential principal component analysis and non-local means based two-stage method for photon-limited Poisson image reconstruction

In this paper, we propose a two-stage method for the Poisson image. Our method is an improvement of the existing two-stage non-local means for Poisson image (Poisson-NLM), which is based on probabilistic similarities to compare noisy patches and patches of a pre-estimated image. In Poisson-NLM, the pre-estimated image is obtained by using simple Gaussian convolution, which is fast but not effective for the image with extremely small number of photons. To overcome this issue, we utilize the exponential non-local principal component analysis based method (NLPCA) to obtain a pre-estimated image at the first stage, and propose a recombined two-stage method called NLPCA-NLM for the reconstruction of photon-limited Poisson image. The numerical experiments show that our method improves the result both visually and in terms of the PSNR and SSIM efficiently, especially for the Poisson images with extremely small number of photons.