G. Kail, J. Tourneret, F. Hlawatsch, and N. Dobigeon, Blind Deconvolution of Sparse Pulse Sequences Under a Minimum Distance Constraint: A Partially Collapsed Gibbs Sampler Method, IEEE Transactions on Signal Processing, vol.60, issue.6, pp.2727-2743, 2012.
DOI : 10.1109/TSP.2012.2190066

L. Wei and M. Levoy, Fast texture synthesis using tree-structured vector quantization, Proceedings of the 27th annual conference on Computer graphics and interactive techniques , SIGGRAPH '00, pp.479-488, 2000.
DOI : 10.1145/344779.345009

URL : http://www.cs.stevens.edu/~quynh/courses/cs638-papers/wei_textsyn.pdf

F. Zhou, J. Feng, and Q. Shi, Texture feature based on local Fourier transform, Proc. Int. Conf. Image Process, pp.610-613, 2001.

G. Xia, S. Ferradans, G. Peyré, and J. Aujol, Synthesizing and Mixing Stationary Gaussian Texture Models, SIAM Journal on Imaging Sciences, vol.7, issue.1, pp.476-508, 2014.
DOI : 10.1137/130918010

URL : https://hal.archives-ouvertes.fr/hal-00988761

M. N. Do and M. Vetterli, Rotation invariant texture characterization and retrieval using steerable wavelet-domain hidden Markov models, IEEE Transactions on Multimedia, vol.4, issue.4, pp.517-527, 2002.
DOI : 10.1109/TMM.2002.802019

URL : https://infoscience.epfl.ch/record/33833/files/DoV02d.pdf

J. Portilla and E. P. Simoncelli, A parametric texture model based on joint statistics of complex wavelet coefficients, International Journal of Computer Vision, vol.40, issue.1, pp.49-71, 2000.
DOI : 10.1023/A:1026553619983

R. Chellappa and S. Chatterjee, Classification of textures using Gaussian Markov random fields, ASSP-33, pp.959-963, 1985.
DOI : 10.1109/TASSP.1985.1164641

R. Chellappa and R. Kashyap, Texture synthesis using 2-D noncausal autoregressive models, IEEE Transactions on Acoustics, Speech, and Signal Processing, vol.33, issue.1, pp.194-203, 1985.
DOI : 10.1109/TASSP.1985.1164507

S. C. Zhu, Y. Wu, and D. Mumford, Filters, random fields and maximum entropy (frame)?Towards a unified theory for texture modeling, Int. J. Comput. Vis, vol.27, issue.2, pp.1-20, 1998.

E. P. Simoncelli, Statistical Modeling of Photographic Images, Handbook of Video and Image Processing, 2005.
DOI : 10.1016/B978-012119792-6/50089-9

H. Akaike, A new look at the statistical model identification, IEEE Transactions on Automatic Control, vol.19, issue.6, pp.716-723, 1974.
DOI : 10.1109/TAC.1974.1100705

S. D. Spiegelhalter, N. G. Best, B. P. Carlin, and A. V. Linde, Bayesian measures of model complexity and fit, Journal of the Royal Statistical Society: Series B (Statistical Methodology), vol.93, issue.4, pp.583-639, 2002.
DOI : 10.1002/1097-0258(20000915/30)19:17/18<2265::AID-SIM568>3.0.CO;2-6

G. Schwarz, Estimating the Dimension of a Model, The Annals of Statistics, vol.6, issue.2, pp.461-464, 1978.
DOI : 10.1214/aos/1176344136

M. J. Beal, Variational algorithms for approximate bayesian inference, 2003.

A. E. Raftery, Hypothesis testing and model selection via posterior simulation, 1995.

J. Rosenthal, Optimal Proposal Distributions and Adaptive MCMC, pp.93-112, 2011.
DOI : 10.1201/b10905-5

URL : http://probability.ca/jeff/ftpdir/galinart.pdf

B. Cai, R. Meyer, and F. Perron, Metropolis???Hastings algorithms with adaptive proposals, Statistics and Computing, vol.18, issue.3, pp.421-433, 2008.
DOI : 10.1007/978-1-4615-3598-0

G. Roberts and O. Stramer, Langevin diffusions and Metropolis-Hastings algorithms, Methodology and Computing in Applied Probability, vol.4, issue.4, pp.337-358, 2003.
DOI : 10.1023/A:1023562417138

M. Girolami and B. Calderhead, Riemann manifold Langevin and Hamiltonian Monte Carlo methods, Journal of the Royal Statistical Society: Series B (Statistical Methodology), vol.13, issue.10, pp.123-214, 2011.
DOI : 10.1162/08997660460734047

URL : http://www.stat.columbia.edu/%7Ecook/movabletype/mlm/RMHMC_MG_BC_SC_REV_08_04_10.pdf

R. M. Neal, MCMC Using Hamiltonian Dynamics, pp.93-112, 2011.
DOI : 10.1201/b10905-6

URL : http://www.mcmchandbook.net/HandbookChapter5.pdf

S. Amari, Natural Gradient Works Efficiently in Learning, Neural Computation, vol.37, issue.2, pp.251-276, 1998.
DOI : 10.1103/PhysRevLett.76.2188

Y. Qi and T. P. Minka, Hessian-based Markov Chain Monte-Carlo algorithms, " presented at the 1st Cape Cod Workshop Monte Carlo Methods, 2002.

A. Ghattas, Scaled stochastic Newton algorithm for Markov chain Monte Carlo simulations, 2012.

J. Martin, L. C. Wilcox, C. Burstedde, and O. Ghattas, A Stochastic Newton MCMC Method for Large-Scale Statistical Inverse Problems with Application to Seismic Inversion, SIAM Journal on Scientific Computing, vol.34, issue.3, pp.1460-1487, 2012.
DOI : 10.1137/110845598

C. Vacar, J. Giovannelli, and Y. Berthoumieu, Langevin and hessian with fisher approximation stochastic sampling for parameter estimation of structured covariance, 2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pp.3964-3967, 2011.
DOI : 10.1109/ICASSP.2011.5947220

URL : https://hal.archives-ouvertes.fr/hal-00668308

C. P. Robert, The Bayesian Choice: From Decision-Theoretic Foundations to Computational Implementation, ser. Springer Texts in Statist, 2007.
DOI : 10.1007/978-1-4757-4314-2

C. Vacar, J. Giovannelli, and A. Roman, Bayesian texture model selection using harmonic mean, 2012.
DOI : 10.1109/icip.2012.6467414

D. Geman and C. Yang, Nonlinear image recovery with half-quadratic regularization, IEEE Transactions on Image Processing, vol.4, issue.7, pp.932-946, 1995.
DOI : 10.1109/83.392335

URL : http://www.math.umass.edu/~geman/Papers/nonlinear.ps.gz

D. Geman and G. Reynolds, Constrained restoration and the recovery of discontinuities, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.14, issue.3, pp.367-383, 1992.
DOI : 10.1109/34.120331

J. F. Giovannelli, Unsupervised Bayesian Convex Deconvolution Based on a Field With an Explicit Partition Function, IEEE Transactions on Image Processing, vol.17, issue.1, pp.16-26, 2008.
DOI : 10.1109/TIP.2007.911819

URL : https://hal.archives-ouvertes.fr/hal-00879198

J. M. Bioucas-dias, Bayesian wavelet-based image deconvolution: a GEM algorithm exploiting a class of heavy-tailed priors, IEEE Transactions on Image Processing, vol.15, issue.4, pp.937-951, 2006.
DOI : 10.1109/TIP.2005.863972

Y. Zhang and N. Kingsbury, Image deconvolution using a Gaussian scale mixtures model to approximate the wavelet sparseness constraint, Proc. IEEE ICASSP, pp.681-684, 2009.

M. J. Wainwright, E. P. Simoncelli, and A. S. Willsky, Random Cascades on Wavelet Trees and Their Use in Analyzing and Modeling Natural Images, Applied and Computational Harmonic Analysis, vol.11, issue.1, pp.89-123, 2001.
DOI : 10.1006/acha.2000.0350

J. Portilla, V. Strela, M. J. Wainwright, and E. P. Simoncelli, Image denoising using scale mixtures of gaussians in the wavelet domain, IEEE Transactions on Image Processing, vol.12, issue.11, pp.1338-1351, 2003.
DOI : 10.1109/TIP.2003.818640

D. K. Hammond and E. P. Simoncelli, Image Modeling and Denoising With Orientation-Adapted Gaussian Scale Mixtures, IEEE Transactions on Image Processing, vol.17, issue.11, pp.2089-2101, 2008.
DOI : 10.1109/TIP.2008.2004796

URL : http://www.cns.nyu.edu/pub/lcv/hammond08-reprint.pdf

H. Rue and L. Held, Gaussian Markov Random Fields: Theory and Applications, Monographs on Statist. Appl. Probabil, vol.104, 2005.
DOI : 10.1201/9780203492024

X. Guyon, Random Fields on a Network: Modelling, Statistics, and Applications, Probability and Its Applications, 1995.

A. Oppenheim and A. S. Willsky, Signals and Systems, 1983.

B. Picinbono, Principles of Signals and Systems: Deterministic Signals, 1988.

J. Skilling, Nested sampling for general Bayesian computation, Bayesian Analysis, vol.1, issue.4, 2006.
DOI : 10.1214/06-BA127

URL : http://doi.org/10.1214/06-ba127

P. J. Green, Reversible jump Markov chain Monte Carlo computation and Bayesian model determination, Biometrika, vol.82, issue.4, pp.711-732, 1995.
DOI : 10.1093/biomet/82.4.711

A. E. Gelfand and D. K. Dey, Bayesian model choice: Asymptotics and exact calculations, J. Roy. Statist. Soc. B, vol.56, issue.3, pp.501-514, 1994.
DOI : 10.21236/ADA269067

URL : http://www.dtic.mil/dtic/tr/fulltext/u2/a269067.pdf

M. A. Newton and A. E. Raftery, Approximate Bayesian inference with the weighted likelihood bootstrap, J. Roy. Stat. Soc. B, vol.56, issue.1, pp.3-48, 1994.

A. G. Pakes, On the convergence of moments of geometric and harmonic means, Statistica Neerlandica, vol.53, issue.1, pp.96-110, 1999.
DOI : 10.1111/1467-9574.00100

A. E. Raftery, M. A. Newton, J. M. Satagopan, and P. N. Krivitsky, Estimating the integrated likelihood via posterior simulation using the harmonic mean identity, Bayesian Statist, pp.1-45, 2007.

R. E. Kass and A. E. Raftery, Bayes Factors, Journal of the American Statistical Association, vol.2, issue.430, pp.773-795, 1995.
DOI : 10.1214/ss/1177013241

C. P. Robert and G. Casella, Monte Carlo Statistical Methods, 2004.

L. Tierney, Markov Chains for Exploring Posterior Distributions, The Annals of Statistics, vol.22, issue.4, pp.1701-1762, 1994.
DOI : 10.1214/aos/1176325750

URL : http://doi.org/10.1214/aos/1176325750

C. P. Robert and G. Casella, Monte-Carlo Statistical Methods, ser. Springer Texts in Statistics, 2004.

F. Orieux, J. F. Giovannelli, and T. Rodet, Bayesian estimation of regularization and point spread function parameters for Wiener???Hunt deconvolution, Journal of the Optical Society of America A, vol.27, issue.7, pp.1593-1607, 2010.
DOI : 10.1364/JOSAA.27.001593

URL : https://hal.archives-ouvertes.fr/hal-00674508

C. Vacar, J. Giovannelli, and Y. Berthoumieu, Bayesian Texture and Instrument Parameter Estimation From Blurred and Noisy Images Using MCMC, IEEE Signal Processing Letters, vol.21, issue.6, pp.707-711, 2014.
DOI : 10.1109/LSP.2014.2313274

URL : https://hal.archives-ouvertes.fr/hal-00975094

G. Kail, J. Tourneret, F. Hlawatsch, and N. Dobigeon, Blind Deconvolution of Sparse Pulse Sequences Under a Minimum Distance Constraint: A Partially Collapsed Gibbs Sampler Method, IEEE Transactions on Signal Processing, vol.60, issue.6, pp.2727-2743, 2012.
DOI : 10.1109/TSP.2012.2190066

L. Wei and M. Levoy, Fast texture synthesis using tree-structured vector quantization, Proceedings of the 27th annual conference on Computer graphics and interactive techniques , SIGGRAPH '00, pp.479-488, 2000.
DOI : 10.1145/344779.345009

URL : http://www.cs.stevens.edu/~quynh/courses/cs638-papers/wei_textsyn.pdf

F. Zhou, J. Feng, and Q. Shi, Texture feature based on local Fourier transform, Proc. Int. Conf. Image Process, pp.610-613, 2001.

G. Xia, S. Ferradans, G. Peyré, and J. Aujol, Synthesizing and Mixing Stationary Gaussian Texture Models, SIAM Journal on Imaging Sciences, vol.7, issue.1, pp.476-508, 2014.
DOI : 10.1137/130918010

URL : https://hal.archives-ouvertes.fr/hal-00988761

M. N. Do and M. Vetterli, Rotation invariant texture characterization and retrieval using steerable wavelet-domain hidden Markov models, IEEE Transactions on Multimedia, vol.4, issue.4, pp.517-527, 2002.
DOI : 10.1109/TMM.2002.802019

URL : https://infoscience.epfl.ch/record/33833/files/DoV02d.pdf

J. Portilla and E. P. Simoncelli, A parametric texture model based on joint statistics of complex wavelet coefficients, International Journal of Computer Vision, vol.40, issue.1, pp.49-71, 2000.
DOI : 10.1023/A:1026553619983

R. Chellappa and S. Chatterjee, Classification of textures using Gaussian Markov random fields, ASSP-33, pp.959-963, 1985.
DOI : 10.1109/TASSP.1985.1164641

R. Chellappa and R. Kashyap, Texture synthesis using 2-D noncausal autoregressive models, IEEE Transactions on Acoustics, Speech, and Signal Processing, vol.33, issue.1, pp.194-203, 1985.
DOI : 10.1109/TASSP.1985.1164507

S. C. Zhu, Y. Wu, and D. Mumford, Filters, random fields and maximum entropy (frame)?Towards a unified theory for texture modeling, Int. J. Comput. Vis, vol.27, issue.2, pp.1-20, 1998.

E. P. Simoncelli, Statistical Modeling of Photographic Images, Handbook of Video and Image Processing, 2005.
DOI : 10.1016/B978-012119792-6/50089-9

H. Akaike, A new look at the statistical model identification, IEEE Transactions on Automatic Control, vol.19, issue.6, pp.716-723, 1974.
DOI : 10.1109/TAC.1974.1100705

S. D. Spiegelhalter, N. G. Best, B. P. Carlin, and A. V. Linde, Bayesian measures of model complexity and fit, Journal of the Royal Statistical Society: Series B (Statistical Methodology), vol.93, issue.4, pp.583-639, 2002.
DOI : 10.1002/1097-0258(20000915/30)19:17/18<2265::AID-SIM568>3.0.CO;2-6

G. Schwarz, Estimating the Dimension of a Model, The Annals of Statistics, vol.6, issue.2, pp.461-464, 1978.
DOI : 10.1214/aos/1176344136

M. J. Beal, Variational algorithms for approximate bayesian inference, 2003.

A. E. Raftery, Hypothesis testing and model selection via posterior simulation, 1995.

J. Rosenthal, Optimal Proposal Distributions and Adaptive MCMC, pp.93-112, 2011.
DOI : 10.1201/b10905-5

URL : http://probability.ca/jeff/ftpdir/galinart.pdf

B. Cai, R. Meyer, and F. Perron, Metropolis???Hastings algorithms with adaptive proposals, Statistics and Computing, vol.18, issue.3, pp.421-433, 2008.
DOI : 10.1007/978-1-4615-3598-0

G. Roberts and O. Stramer, Langevin diffusions and Metropolis-Hastings algorithms, Methodology and Computing in Applied Probability, vol.4, issue.4, pp.337-358, 2003.
DOI : 10.1023/A:1023562417138

M. Girolami and B. Calderhead, Riemann manifold Langevin and Hamiltonian Monte Carlo methods, Journal of the Royal Statistical Society: Series B (Statistical Methodology), vol.13, issue.10, pp.123-214, 2011.
DOI : 10.1162/08997660460734047

URL : http://www.stat.columbia.edu/%7Ecook/movabletype/mlm/RMHMC_MG_BC_SC_REV_08_04_10.pdf

R. M. Neal, MCMC Using Hamiltonian Dynamics, pp.93-112, 2011.
DOI : 10.1201/b10905-6

URL : http://www.mcmchandbook.net/HandbookChapter5.pdf

S. Amari, Natural Gradient Works Efficiently in Learning, Neural Computation, vol.37, issue.2, pp.251-276, 1998.
DOI : 10.1103/PhysRevLett.76.2188

Y. Qi and T. P. Minka, Hessian-based Markov Chain Monte-Carlo algorithms, " presented at the 1st Cape Cod Workshop Monte Carlo Methods, 2002.

A. Ghattas, Scaled stochastic Newton algorithm for Markov chain Monte Carlo simulations, 2012.

J. Martin, L. C. Wilcox, C. Burstedde, and O. Ghattas, A Stochastic Newton MCMC Method for Large-Scale Statistical Inverse Problems with Application to Seismic Inversion, SIAM Journal on Scientific Computing, vol.34, issue.3, pp.1460-1487, 2012.
DOI : 10.1137/110845598

C. Vacar, J. Giovannelli, and Y. Berthoumieu, Langevin and hessian with fisher approximation stochastic sampling for parameter estimation of structured covariance, 2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pp.3964-3967, 2011.
DOI : 10.1109/ICASSP.2011.5947220

URL : https://hal.archives-ouvertes.fr/hal-00668308

C. P. Robert, The Bayesian Choice: From Decision-Theoretic Foundations to Computational Implementation, ser. Springer Texts in Statist, 2007.
DOI : 10.1007/978-1-4757-4314-2

C. Vacar, J. Giovannelli, and A. Roman, Bayesian texture model selection using harmonic mean, 2012.
DOI : 10.1109/icip.2012.6467414

D. Geman and C. Yang, Nonlinear image recovery with half-quadratic regularization, IEEE Transactions on Image Processing, vol.4, issue.7, pp.932-946, 1995.
DOI : 10.1109/83.392335

URL : http://www.math.umass.edu/~geman/Papers/nonlinear.ps.gz

D. Geman and G. Reynolds, Constrained restoration and the recovery of discontinuities, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.14, issue.3, pp.367-383, 1992.
DOI : 10.1109/34.120331

J. F. Giovannelli, Unsupervised Bayesian Convex Deconvolution Based on a Field With an Explicit Partition Function, IEEE Transactions on Image Processing, vol.17, issue.1, pp.16-26, 2008.
DOI : 10.1109/TIP.2007.911819

URL : https://hal.archives-ouvertes.fr/hal-00879198

J. M. Bioucas-dias, Bayesian wavelet-based image deconvolution: a GEM algorithm exploiting a class of heavy-tailed priors, IEEE Transactions on Image Processing, vol.15, issue.4, pp.937-951, 2006.
DOI : 10.1109/TIP.2005.863972

Y. Zhang and N. Kingsbury, Image deconvolution using a Gaussian scale mixtures model to approximate the wavelet sparseness constraint, Proc. IEEE ICASSP, pp.681-684, 2009.

M. J. Wainwright, E. P. Simoncelli, and A. S. Willsky, Random Cascades on Wavelet Trees and Their Use in Analyzing and Modeling Natural Images, Applied and Computational Harmonic Analysis, vol.11, issue.1, pp.89-123, 2001.
DOI : 10.1006/acha.2000.0350

J. Portilla, V. Strela, M. J. Wainwright, and E. P. Simoncelli, Image denoising using scale mixtures of gaussians in the wavelet domain, IEEE Transactions on Image Processing, vol.12, issue.11, pp.1338-1351, 2003.
DOI : 10.1109/TIP.2003.818640

D. K. Hammond and E. P. Simoncelli, Image Modeling and Denoising With Orientation-Adapted Gaussian Scale Mixtures, IEEE Transactions on Image Processing, vol.17, issue.11, pp.2089-2101, 2008.
DOI : 10.1109/TIP.2008.2004796

URL : http://www.cns.nyu.edu/pub/lcv/hammond08-reprint.pdf

H. Rue and L. Held, Gaussian Markov Random Fields: Theory and Applications, Monographs on Statist. Appl. Probabil, vol.104, 2005.
DOI : 10.1201/9780203492024

X. Guyon, Random Fields on a Network: Modelling, Statistics, and Applications, Probability and Its Applications, 1995.

A. Oppenheim and A. S. Willsky, Signals and Systems, 1983.

B. Picinbono, Principles of Signals and Systems: Deterministic Signals, 1988.

J. Skilling, Nested sampling for general Bayesian computation, Bayesian Analysis, vol.1, issue.4, 2006.
DOI : 10.1214/06-BA127

URL : http://doi.org/10.1214/06-ba127

P. J. Green, Reversible jump Markov chain Monte Carlo computation and Bayesian model determination, Biometrika, vol.82, issue.4, pp.711-732, 1995.
DOI : 10.1093/biomet/82.4.711

A. E. Gelfand and D. K. Dey, Bayesian model choice: Asymptotics and exact calculations, J. Roy. Statist. Soc. B, vol.56, issue.3, pp.501-514, 1994.
DOI : 10.21236/ADA269067

URL : http://www.dtic.mil/dtic/tr/fulltext/u2/a269067.pdf

M. A. Newton and A. E. Raftery, Approximate Bayesian inference with the weighted likelihood bootstrap, J. Roy. Stat. Soc. B, vol.56, issue.1, pp.3-48, 1994.

A. G. Pakes, On the convergence of moments of geometric and harmonic means, Statistica Neerlandica, vol.53, issue.1, pp.96-110, 1999.
DOI : 10.1111/1467-9574.00100

A. E. Raftery, M. A. Newton, J. M. Satagopan, and P. N. Krivitsky, Estimating the integrated likelihood via posterior simulation using the harmonic mean identity, Bayesian Statist, pp.1-45, 2007.

R. E. Kass and A. E. Raftery, Bayes Factors, Journal of the American Statistical Association, vol.2, issue.430, pp.773-795, 1995.
DOI : 10.1214/ss/1177013241

C. P. Robert and G. Casella, Monte Carlo Statistical Methods, 2004.

L. Tierney, Markov Chains for Exploring Posterior Distributions, The Annals of Statistics, vol.22, issue.4, pp.1701-1762, 1994.
DOI : 10.1214/aos/1176325750

URL : http://doi.org/10.1214/aos/1176325750

C. P. Robert and G. Casella, Monte-Carlo Statistical Methods, ser. Springer Texts in Statistics, 2004.

F. Orieux, J. F. Giovannelli, and T. Rodet, Bayesian estimation of regularization and point spread function parameters for Wiener???Hunt deconvolution, Journal of the Optical Society of America A, vol.27, issue.7, pp.1593-1607, 2010.
DOI : 10.1364/JOSAA.27.001593

URL : https://hal.archives-ouvertes.fr/hal-00674508

C. Vacar, J. Giovannelli, and Y. Berthoumieu, Bayesian Texture and Instrument Parameter Estimation From Blurred and Noisy Images Using MCMC, IEEE Signal Processing Letters, vol.21, issue.6, pp.707-711, 2014.
DOI : 10.1109/LSP.2014.2313274

URL : https://hal.archives-ouvertes.fr/hal-00975094