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Research Article

A blocking scheme for dimension-robust Gibbs sampling in large-scale image deblurring

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Pages 1789-1810 | Received 09 Sep 2020, Accepted 13 Jan 2021, Published online: 05 Feb 2021

References

  • Halls BR, Roy S, Gord JR, et al. Quantitative imaging of single-shot liquid distributions in sprays using broadband flash X-ray radiography. Int J Multiphase Flow. 2016;87:241–249.
  • Hanson KM, Cunningham GS. The Bayes inference engine. In: Maximum entropy and Bayesian methods. Dordrecht, The Netherlands: Kluwer Academic; 1996. p. 125–134.
  • Howard M, Fowler M, Luttman A, et al. Bayesian Abel inversion in quantitative X-ray radiography. SIAM J Sci Comput. 2016;38:B396–B413.
  • Maire E, Withers PJ. Quantitative X-ray tomography. Int Mater Rev. 2014;59:1–43.
  • Fowler M, Howard M, Luttman A, et al. A stochastic approach to quantifying the blur with uncertainty estimation for high-energy X-ray imaging systems. Inverse Probl Sci Eng. 2016;24:353–371.
  • Nagesh SVS, Rana R, Russ M, Ionita CN, Bednarek DR, Rudin S. Focal spot deblurring for high resolution direct conversion x-ray detectors. Proc SPIE Int Soc Opt Eng. 2016;9783:97833R.
  • von Wittenau AES, Logan CM, Aufderheide MB, et al. Blurring artifacts in megavoltage radiography with a flat-panel imaging system: comparison of Monte Carlo simulations with measurements. Med Phys. 2002;29:2559–2570.
  • Hansen PC, Nagy JG, O'Leary DP. Deblurring images: matrices, spectra, and filtering. Philadelphia, PA: SIAM; 2006.
  • Bardsley JM. Computational uncertainty quantification for inverse problems. Philadelphia (PA): SIAM; 2018.
  • Bardsley JM, Luttman A. Dealing with boundary artifacts in MCMC-based deconvolution. Linear Algebra Appl. 2015;473:339–358.
  • Bardsley JM, Luttman A. A Metropolis-Hastings method for linear inverse problems with Poisson likelihood and Gaussian prior. Int J Uncertain Quantif. 2016;6:35–55.
  • Fox C, Norton RA. Fast sampling in a linear-Gaussian inverse problem. SIAM/ASA J Uncertain Quantif. 2016;4:1191–1218.
  • Fox C, Parker A. Accelerated Gibbs sampling of normal distributions using matrix splittings and polynomials. Bernoulli. 2017;23:3711–3743.
  • Howard M, Fowler M, Luttman A. Sampling-based uncertainty quantification in deconvolution of X-ray radiographs. J Comput Appl Math. 2014;270:43–51.
  • Joyce KT, Bardsley JM, Luttman A. Point spread function estimation in X-ray imaging with partially collapsed Gibbs sampling. SIAM J Sci Comput. 2018;40:B766–B787.
  • Wang Z, Bardsley J, Solonen A, et al. Bayesian inverse problems with ℓ1 priors: a randomize-then-optimize approach. SIAM J Sci Comput. 2017;39:S140–S166.
  • Parker A, Pitts B, Lorenz L, et al. Polynomial accelerated solutions to a large gaussian model for imaging biofilms: in theory and finite precision. J Am Stat Assoc. 2018;113:1431–1442.
  • Chen J, Anitescu M, Saad Y. Computing f(a)b via least squares polynomial approximations. SIAM J Sci Comput. 2011;33:195–222.
  • Chow E, Saad Y. Preconditioned krylov subspace methods for sampling multivariate gaussian distributions. SIAM J Sci Comput. 2014;36:A588–A608.
  • Parker A, Fox C. Sampling gaussian distributions in krylov spaces with conjugate gradients. SIAM J Sci Comput. 2012;34:B312–B334.
  • Gilks W, Richardson S, Spiegelhalter D. Markov chain Monte Carlo in practice. Boca Raton, FL: Springer; 1996.
  • Rubinstein RY, Kroese DP. Simulation and the Monte Carlo method. 3rd ed. Hoboken, NJ: Wiley; 2017.
  • Morzfeld M, Tong X, Marzouk YM. Localization for MCMC: sampling high-dimensional posterior distributions with local structure. J Comput Phys. 2018;380:1–28.
  • Roberts GO, Sahu S. Updating schemes, correlation structure, blocking and parameterization for the Gibbs sampler. J R Stat Soc Ser B. 1997;59:291–317.
  • Chen V, Dunlop MM, Papaspiliopoulos O, et al. Dimension-robust MCMC in Bayesian inverse problems. Submitted; 2018.
  • Beskos A, Roberts G, Stuart A. Optimal scalings for local Metropolis-Hastings chains on nonproduct targets in high dimensions. Ann Appl Probab. 2009;19:863–898.
  • Roberts G, Gelman A, Gilks W. Weak convergence and optimal scaling of random walk Metropolis algorithms. Ann Appl Probab. 1997;7:110–120.
  • Roberts G, Rosenthal J. Optimal scaling of discrete approximations to Langevin diffusions. J R Stat Soc, Ser B (Stat Methodol). 1998;60:255–268.
  • Buccini A, Donatelli M, Reichel L. Iterated Tikhonov regularization with a general penalty term. Numer Linear Algebra Appl. 2017;24:1–19.
  • Chen H, Wang C, Song Y, et al. Split Bregmanized anisotropic total variation model for image deblurring. J Vis Commun Image Represent. 2015;31:282–293.
  • Jiao Y, Jin Q, Lu X, et al. Alternating direction method of multipliers for linear inverse problems. SIAM J Numer Anal. 2016;54:2114–2137.
  • Ma L, Xu L, Zeng T. Low rank prior and total variation regularization for image deblurring. J Sci Comput. 2017;70:1336–1357.
  • Tao S, Dong W, Xu Z, et al. Fast total variation deconvolution for blurred image contaminated by Poisson noise. J Vis Commun Image Represent. 2016;38:582–594.
  • Xu J, Chang HB, Qin J. Domain decomposition method for image deblurring. J Comput Appl Math. 2014;271:401–414.
  • Bertero M, Boccacci P. A simple method for the reduction of boundary effects in the Richardson-Lucy approach to image deconvolution. Astron Astrophys. 2005;437:369–374.
  • Vio R, Bardsley JM, Donatelli M, et al. Dealing with edge effects in least-squares image deconvolution problems. Astron Astrophys. 2005;442:397–403.
  • Bardsley JM. Gaussian Markov random field priors for inverse problems. Inverse Probl Imaging. 2013;7:397–416.
  • Rue H, Held L. Gaussian Markov random fields: theory and applications. New York, NY: Chapman & Hall/CRC; 2005.
  • Gelman A, Carlin JB, Stern HS, et al. Bayesian data analysis. 3rd ed. Boca Raton, FL: Chapman and Hall CRC Press; 2013.
  • Geman S, Geman D. Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images. IEEE Trans Pattern Anal Mach Intell. 1984;PAMI-6:721–741.
  • Adams J. Scalable block-Gibbs sampling for image deblurring in X-ray radiography [PhD dissertation]. Tucson (Arizona): University of Arizona; 2019.
  • Asaki TJ, Chartrand R, Vixie KR, et al. Abel inversion using total-variation regularization. Inverse Probl. 2005;21:1895–1903.
  • Asaki TJ, Campbell PR, Chartrand R, et al. Abel inversion using total variation regularization: applications. Inverse Probl Sci Eng. 2006;14:873–885.
  • Davis G, Jain N, Elliott J. A modelling approach to beam hardening correction. Proc SPIE Int Soc Opt Eng. 2008;7078:70781E.
  • Kwan TJT, Berninger M, Snell C, et al. Simulation of the cygnus rod-pinch diode using the radiographic chain model. IEEE Trans Plasma Sci. 2009;37:530–537.
  • Seeman HE, Roth B. New stepped wedges for radiography. Acta radiol. 1960;53:215–226.
  • Engl H, Hanke M, Neubauer A. Regularization for inverse problems. Dordrecht, The Netherlands: Kluwer Academic; 1996.
  • Golub GH, Heath M, Wahba G. Generalized cross-validation as a method for choosing a good ridge parameter. Technometrics. 1979;21:215–223.
  • Renaut RA, Helmstetter AW, Vatankhah S. Unbiased predictive risk estimation of the tikhonov regularization parameter: convergence with increasing rank approximations of the singular value decomposition. BIT Numer Math. 2019;59:1031–1061.
  • Vogel CR. Computational methods for inverse problems. Philadelphia (PA): SIAM; 2002.
  • Sokal A. Monte Carlo methods in statistical mechanics: foundations and new algorithms. In: DeWitt-Morette C, Cartier P, Folacci A, editors. Functional Integration. NATO ASI Series (Series B: Physics). Vol. 361. Boston (MA): Springer; 1998.
  • Wolff U. Monte Carlo errors with less errors. Comput Phys Commun. 2004;156:145–153.

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