Three-Dimensional Image Visualization under Photon-Starved Conditions Using <i>N</i> Observations and Statistical Estimation

Abstract

In this paper, we propose a method for the three-dimensional (3D) image visualization of objects under photon-starved conditions using multiple observations and statistical estimation. To visualize 3D objects under these conditions, photon counting integral imaging was used, which can extract photons from 3D objects using the Poisson random process. However, this process may not reconstruct 3D images under severely photon-starved conditions due to a lack of photons. Therefore, to solve this problem, in this paper, we propose N-observation photon-counting integral imaging with statistical estimation. Since photons are extracted randomly using the Poisson distribution, increasing the samples of photons can improve the accuracy of photon extraction. In addition, by using a statistical estimation method, such as maximum likelihood estimation, 3D images can be reconstructed. To prove our proposed method, we implemented the optical experiment and calculated its performance metrics, which included the peak signal-to-noise ratio (PSNR), structural similarity (SSIM), peak-to-correlation energy (PCE), and the peak sidelobe ratio (PSR).

Keywords

• maximum likelihood estimation
• N observations
• photon-counting integral imaging
• three-dimensional imaging
• volumetric computational reconstruction