Robust 3D imaging based on regularization by denoising

Reconstructing a 3D image from the photon echo is a challenging task due to spurious detections associated with large amounts of background counts. Here, we propose a robust method for estimating the depth and reflectivity by using regularization by the denoising method, where the block matching and the 3D filtering are adopted as denoisers, and in the meantime, the steepest-descent method is implemented to solve the optimization problem. Experimental data with different signal-to-background ratios and different numbers of photons verify that our method is able to accurately recover 3D images. Compared with other existing methods, such as the maximum likelihood estimation algorithm, the photon efficient algorithm by Shin et al. [IEEE Trans. Comput. Imaging1, 112 (2015)2333-940310.1109/TCI.2015.2453093], and the ManiPoP algorithm, our method can effectively remove noise while preserving the edge information of depth images, with better depth image estimation and smaller root mean square error, especially at low signal-to-noise ratios. The superiority of this method over other methods is verified on simulated data sets under different conditions.