Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
125 tokens/sec
GPT-4o
47 tokens/sec
Gemini 2.5 Pro Pro
43 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
47 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Projected Multi-Agent Consensus Equilibrium (PMACE) with Application to Ptychography (2303.15679v2)

Published 28 Mar 2023 in math.OC and eess.IV

Abstract: Multi-Agent Consensus Equilibrium (MACE) formulates an inverse imaging problem as a balance among multiple update agents such as data-fitting terms and denoisers. However, each such agent operates on a separate copy of the full image, leading to redundant memory use and slow convergence when each agent affects only a small subset of the full image. In this paper, we extend MACE to Projected Multi-Agent Consensus Equilibrium (PMACE), in which each agent updates only a projected component of the full image, thus greatly reducing memory use for some applications.We describe PMACE in terms of an equilibrium problem and an equivalent fixed point problem and show that in most cases the PMACE equilibrium is not the solution of an optimization problem. To demonstrate the value of PMACE, we apply it to the problem of ptychography, in which a sample is reconstructed from the diffraction patterns resulting from coherent X-ray illumination at multiple overlapping spots. In our PMACE formulation, each spot corresponds to a separate data-fitting agent, with the final solution found as an equilibrium among all the agents. Our results demonstrate that the PMACE reconstruction algorithm generates more accurate reconstructions at a lower computational cost than existing ptychography algorithms when the spots are sparsely sampled.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (35)
  1. K. Dabov, A. Foi, V. Katkovnik, and K. Egiazarian, “Image Denoising by Sparse 3-D Transform-Domain Collaborative Filtering,” IEEE Trans. Image Process., vol. 16, no. 8, pp. 2080–2095, 2007.
  2. K. Zhang, W. Zuo, Y. Chen, D. Meng, and L. Zhang, “Beyond a Gaussian denoiser: Residual learning of deep CNN for image denoising,” IEEE transactions on image processing, vol. 26, no. 7, pp. 3142–3155, 2017.
  3. G. T. Buzzard, S. H. Chan, S. Sreehari, and C. A. Bouman, “Plug-and-play unplugged: Optimization-free reconstruction using consensus equilibrium,” SIAM Journal on Imaging Sciences, vol. 11, no. 3, pp. 2001–2020, 2018.
  4. S. V. Venkatakrishnan, C. A. Bouman, and B. Wohlberg, “Plug-and-Play priors for model based reconstruction,” in 2013 IEEE Global Conference on Signal and Information Processing, Dec. 2013, pp. 945–948.
  5. S. Sreehari, S. V. Venkatakrishnan, B. Wohlberg, G. T. Buzzard, L. F. Drummy, J. P. Simmons, and C. A. Bouman, “Plug-and-play priors for bright field electron tomography and sparse interpolation,” Transactions on Computational Imaging, vol. 2, pp. 408–423, 2016.
  6. J. M. Rodenburg, “Ptychography and related diffractive imaging methods,” Advances in imaging and electron physics, vol. 150, pp. 87–184, 2008.
  7. J. Rodenburg and A. Maiden, “Ptychography,” Springer Handbook of Microscopy, pp. 819–904, 2019.
  8. R. Wilke, M. Priebe, M. Bartels, K. Giewekemeyer, A. Diaz, P. Karvinen, and T. Salditt, “Hard x-ray imaging of bacterial cells: nano-diffraction and ptychographic reconstruction,” Optics express, vol. 20, no. 17, pp. 19 232–19 254, 2012.
  9. P. Trtik, A. Diaz, M. Guizar-Sicairos, A. Menzel, and O. Bunk, “Density mapping of hardened cement paste using ptychographic x-ray computed tomography,” Cement and Concrete Composites, vol. 36, pp. 71–77, 2013.
  10. M. Guizar-Sicairos, I. Johnson, A. Diaz, M. Holler, P. Karvinen, H.-C. Stadler, R. Dinapoli, O. Bunk, and A. Menzel, “High-throughput ptychography using eiger: scanning x-ray nano-imaging of extended regions,” Optics express, vol. 22, no. 12, pp. 14 859–14 870, 2014.
  11. D. A. Shapiro, R. Celestre, P. Denes, M. Farmand, J. Joseph, A. Kilcoyne, S. Marchesini, H. Padmore, S. V. Venkatakrishnan, T. Warwick et al., “Ptychographic imaging of nano-materials at the advanced light source with the nanosurveyor instrument,” in Journal of Physics: Conference Series, vol. 849, no. 1, 2017, p. 012028.
  12. J. R. Fienup, “Phase retrieval algorithms: a comparison,” Applied Optics, vol. 21, no. 15, pp. 2758–2769, 1982.
  13. J. M. Rodenburg and H. M. Faulkner, “A phase retrieval algorithm for shifting illumination,” Applied Physics Letters, vol. 85, no. 20, pp. 4795–4797, 2004.
  14. A. M. Maiden and J. M. Rodenburg, “An improved ptychographical phase retrieval algorithm for diffractive imaging,” Ultramicroscopy, vol. 109, no. 10, pp. 1256–1262, 2009.
  15. P. Thibault and A. Menzel, “Reconstructing state mixtures from diffraction measurements,” Nature, vol. 494, no. 7435, pp. 68–71, Feb. 2013. [Online]. Available: https://doi.org/10.1038/nature11806
  16. A. Maiden, D. Johnson, and P. Li, “Further improvements to the ptychographical iterative engine,” Optica, vol. 4, no. 7, pp. 736–745, 2017.
  17. O. Bunk, M. Dierolf, S. Kynde, I. Johnson, O. Marti, and F. Pfeiffer, “Influence of the overlap parameter on the convergence of the ptychographical iterative engine,” Ultramicroscopy, vol. 108, no. 5, pp. 481–487, 2008.
  18. E. J. Candes, X. Li, and M. Soltanolkotabi, “Phase retrieval via Wirtinger flow: Theory and algorithms,” IEEE Transactions on Information Theory, vol. 61, no. 4, pp. 1985–2007, 2015.
  19. R. Xu, M. Soltanolkotabi, J. P. Haldar, W. Unglaub, J. Zusman, A. F. Levi, and R. M. Leahy, “Accelerated Wirtinger flow: A fast algorithm for ptychography,” arXiv preprint arXiv:1806.05546, 2018.
  20. M. Odstrčil, A. Menzel, and M. Guizar-Sicairos, “Iterative least-squares solver for generalized maximum-likelihood ptychography,” Optics Express, vol. 26, no. 3, pp. 3108–3123, 2018.
  21. F. Soulez, É. Thiébaut, A. Schutz, A. Ferrari, F. Courbin, and M. Unser, “Proximity operators for phase retrieval,” Applied optics, vol. 55, no. 26, pp. 7412–7421, 2016.
  22. H. Yan, “Ptychographic phase retrieval by proximal algorithms,” New Journal of Physics, vol. 22, no. 2, p. 023035, 2020.
  23. S. Marchesini, Y.-C. Tu, and H.-t. Wu, “Alternating projection, ptychographic imaging and phase synchronization,” Applied and Computational Harmonic Analysis, vol. 41, no. 3, pp. 815–851, 2016.
  24. S. Marchesini, H. Krishnan, B. J. Daurer, D. A. Shapiro, T. Perciano, J. A. Sethian, and F. R. Maia, “SHARP: a distributed GPU-based ptychographic solver,” Journal of Applied Crystallography, vol. 49, no. 4, pp. 1245–1252, 2016.
  25. D. R. Luke, “Relaxed averaged alternating reflections for diffraction imaging,” Inverse Problems, vol. 21, no. 1, p. 37, 2004.
  26. V. Sridhar, X. Wang, G. T. Buzzard, and C. A. Bouman, “Distributed iterative ct reconstruction using multi-agent consensus equilibrium,” IEEE Transactions on Computational Imaging, vol. 6, pp. 1153–1166, 2020.
  27. R. E. Williamson and H. F. Trotter, “Multivariable mathematics: Linear algebra, calculus,” Differential Equations, vol. 2, no. 4, 2004.
  28. P. L. Combettes, “Monotone operator theory in convex optimization,” Mathematical Programming, vol. 170, no. 1, pp. 177–206, Jul. 2018. [Online]. Available: https://doi.org/10.1007/s10107-018-1303-3
  29. H. H. Bauschke and P. L. Combettes, “Convex analysis and monotone operator theory in Hilbert spaces,” in CMS Books in Mathematics, 2011.
  30. S. V. Venkatakrishnan, C. A. Bouman, and B. Wohlberg, “Plug-and-play priors for model based reconstruction,” in IEEE Global Conference on Signal and Information Processing.   IEEE, 2013, pp. 945–948.
  31. P. Godard, M. Allain, V. Chamard, and J. Rodenburg, “Noise models for low counting rate coherent diffraction imaging,” Optics Express, vol. 20, no. 23, pp. 25 914–25 934, 2012.
  32. X. Huang, H. Yan, R. Harder, Y. Hwu, I. K. Robinson, and Y. S. Chu, “Optimization of overlap uniformness for ptychography,” Optics Express, vol. 22, no. 10, pp. 12 634–12 644, 2014.
  33. L. Zhou, J. Song, J. S. Kim, X. Pei, C. Huang, M. Boyce, L. Mendonça, D. Clare, A. Siebert, C. S. Allen et al., “Low-dose phase retrieval of biological specimens using cryo-electron ptychography,” Nature Communications, vol. 11, no. 1, pp. 1–9, 2020.
  34. S. Marchesini, “Ptychography gold ball example dataset,” Lawrence Berkeley National Lab. (LBNL), Berkeley, CA, USA, Tech. Rep., 2017.
  35. E. K. Ryu and S. Boyd, “A primer on monotone operator methods survey,” Appl. Comput. Math., vol. 15, no. 1, pp. 3–43, 2016.
Citations (5)
View on Semantic Scholar

Summary

We haven't generated a summary for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Summarize Now