ADMM approach for efficient iterative tomographic deconvolution reconstruction of 3D quantitative phase images.

Tomographic deconvolution phase microscopy (TDPM) is a promising approach for 3D quantitative imaging of phase objects such as biological cells and optical fibers. In the present work, the alternating direction method of multipliers (ADMM) is applied to TDPM to shorten its image acquisition and processing times while simultaneously improving its accuracy. ADMM-TDPM is used to optimize the image fidelity by minimizing Gaussian noise and by using total variation regularization with the constraints of nonnegativity and known zeros. ADMM-TDPM can reconstruct phase objects that are shift variant in three spatial dimensions. ADMM-TDPM achieves speedups of 5x in image acquisition time and greater than 10x in image processing time with accompanying higher accuracy compared to TDPM.