Table of Links I. Introduction I. Introduction II. Maximum Entropy Tomography II. Maximum Entropy Tomography A. Ment B. Ment-Flow A. Ment A. Ment B. Ment-Flow B. Ment-Flow III. Numerical Experiments III. Numerical Experiments A. 2D reconstructions from 1D projections B. 6D reconstructions from 1D projections A. 2D reconstructions from 1D projections A. 2D reconstructions from 1D projections B. 6D reconstructions from 1D projections B. 6D reconstructions from 1D projections IV. Conclusion and Extensions IV. Conclusion and Extensions V. Acknowledgments and References V. Acknowledgments and References A. MENT The MENT algorithm [19–22] leverages a Gauss-Seidel relaxation method to optimize the Lagrange functions in Eq. (6). After initializing the distribution to the prior within the measurement boundaries the Lagrange functions are updated as MENT maximizes entropy by design: fitting the data generates an exact solution to the constrained optimization problem. MENT is also efficient: it stores the exact number of parameters needed to define the maximum-entropy distribution and typically converges in a few epochs. Finally, MENT is essentially free of hyperparameters. The MENT formulation above is valid for n:m tomography, but the integrals in Eq. (9) limit the value of n in practice. Ongoing work aims to demonstrate efficient implementations when n = 4 [19, 23]. Extension to n = 6 may be possible, but it has yet to be demonstrated, and the runtime would likely be quite long if there were many high-resolution measurements. Even if the algorithm converged, sampling particles from the posterior (Eq. (6)) would be a nontrivial extra step n:m n n Authors: (1) Austin Hoover, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37830, USA (hooveram@ornl.gov); (2) Jonathan C. Wong, Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, China. Authors: Authors: (1) Austin Hoover, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37830, USA (hooveram@ornl.gov); (2) Jonathan C. Wong, Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, China. This paper is available on arxiv under CC BY 4.0 DEED license. This paper is available on arxiv under CC BY 4.0 DEED license. available on arxiv available on arxiv
