Hierarchical bayesian sparse image reconstruction with application to MRFM

IEEE Transactions on Image Processing

Volumn 18, Issue 9, 2009, Pages 2059-2070

  Dobigeon, Nicolas ^a,b   Hero, Alfred O ^a   Tourneret, Jean Yves ^b  

^a UNIVERSITY OF MICHIGAN   (United States)

^b UNIVERSITÉ DE TOULOUSE   (France)

Author keywords

Bayesian inference; Deconvolution; Magnetic resonance force microscopy (MRFM) imaging; Markov chain Monte Carlo (MCMC) methods; Sparse representation

Indexed keywords

ADDITIVE WHITE GAUSSIAN NOISE; BAYES MODELS; BAYESIAN APPROACHES; BAYESIAN INFERENCE; EXPONENTIAL DISTRIBUTIONS; GIBBS SAMPLING; HIERARCHICAL BAYESIAN; HIERARCHICAL BAYESIAN MODELS; HYPERPARAMETERS; LINEAR TRANSFORMATION; MAGNETIC RESONANCE FORCE MICROSCOPY (MRFM) IMAGING; MARGINALIZATION; MARKOV CHAIN MONTE CARLO (MCMC) METHODS; POINT ESTIMATE; POSTERIOR DISTRIBUTIONS; SPARSE IMAGES; SPARSE RECONSTRUCTION; SPARSE REPRESENTATION; SYNTHETIC DATA;

CONVOLUTION; GAUSSIAN NOISE (ELECTRONIC); IMAGE RECONSTRUCTION; INFERENCE ENGINES; MAGNETIC FORCE MICROSCOPY; MAGNETIC RESONANCE; MARKOV PROCESSES; MONTE CARLO METHODS; REPAIR; WHITE NOISE;

BAYESIAN NETWORKS;

ALGORITHM; ARTICLE; ARTIFICIAL INTELLIGENCE; ATOMIC FORCE MICROSCOPY; BAYES THEOREM; IMAGE PROCESSING; METHODOLOGY; MONTE CARLO METHOD; NUCLEAR MAGNETIC RESONANCE SPECTROSCOPY; PROBABILITY; TOBACCO MOSAIC VIRUS;

ALGORITHMS; ARTIFICIAL INTELLIGENCE; BAYES THEOREM; IMAGE PROCESSING, COMPUTER-ASSISTED; MAGNETIC RESONANCE SPECTROSCOPY; MARKOV CHAINS; MICROSCOPY, ATOMIC FORCE; MONTE CARLO METHOD; TOBACCO MOSAIC VIRUS;

EID: 69349103766     PISSN: 10577149     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIP.2009.2024067     Document Type: Article

References (58)

1. S. Alliney and S. A. Ruzinsky, "An algorithm for the minimization of mixed L1 and L2 norms with application to Bayesian estimation," IEEE Trans. Signal Process., vol. 42, no. 1, pp. 618-627, Mar. 1994.
2. H. Andrews and B. Hunt, Digital Image Restoration. Englewood Cliffs, NJ: Prentice-Hall, 1977.
3. S. Bourguignon and H. Carfantan, "Bernoulli-Gaussian spectral analysis of unevenly spaced astrophysical data," in Proc. IEEE Workshop on Stat. Signal Processing (SSP), Bordeaux, France, Jul. 2005, pp. 811-816.
4. S. Bourguignon, H. Carfantan, and J. Idier, "A sparsity-based method for the estimation of spectral lines from irregularly sampled data," IEEE J. Sel. Topics Signal Process., vol. 1, no. 4, pp. 575-585, Dec. 2007.
5. F. Champagnat, Y. Goussard, and J. Idier, "Unsupervised deconvolution of sparse spike trains using stochastic approximation," IEEE Trans. Signal Process., vol. 44, no. 12, pp. 2988-2998, Dec. 1996.
6. S. Chao, W. M. Dougherty, J. L. Garbini, and J. A. Sidles, "Nanometer-scale magnetic resonance imaging," Review Sci. Instrum. vol. 75, no. 5, pp. 1175-1181, Apr. 2004.
7. Q. Cheng, R. Chen, and T.-H Li, "Simultaneous wavelet estimation and deconvolution of reflection seismic signals," IEEE Trans. Geosci. Remote Sens., vol. 34, no. 2, pp. 377-384, Mar. 1996.
8. C. L. Degen, M. Poggio, H. J. Mamin, C. T. Rettner, and D. Rugar, "Nanoscale magnetic resonance imaging," Proc. Nat. Acad. Sci., vol. 106, no. 5, pp. 1313-1317, Feb. 2009.
9. C. L. Degen, M. Poggio, H. J. Mamin, C. T. Rettner, and D. Rugar, "Nanoscale magnetic resonance imaging. Supporting information," Proc. Nat. Acad. Sci., vol. 106, no. 5, Feb. 2009.
10. J. Diebolt and E. H. S. Ip, "Stochastic EM: Method and application," in Markov Chain Monte Carlo in Practice, W. R. Gilks, S. Richardson, and D. J. Spiegelhalter, Eds. London, U.K.: Chapman & Hall, 1996, pp. 259-273.
11. N. Dobigeon and J.-Y. Tourneret, "Joint segmentation of wind speed and direction using a hierarchical model," Comput. Stat. Data Anal., vol. 51, no. 12, pp. 5603-5621, Aug. 2007.
12. N. Dobigeon and J.-Y. Tourneret, "Bayesian sampling of structured noise covariance matrix for hyperspectral imagery," Tech. Rep., Univ. Toulouse, France, Dec. 2008 [Online]. Available: http:// dobigeon.perso.enseeiht.fr/publis.html
13. N. Dobigeon, J.-Y. Tourneret, and C.-I Chang, "Semi-supervised linear spectral unmixing using a hierarchical Bayesian model for hyperspectral imagery," IEEE Trans. Signal Process., vol. 56, no. 7, pp. 2684-2695, Jul. 2008.
14. N. Dobigeon, J.-Y. Tourneret, and M. Davy, "Joint segmentation of piecewise constant autoregressive processes processes by using a hierarchical model and a Bayesian sampling approach," IEEE Trans. Signal Process., vol. 55, no. 4, pp. 1251-1263, Apr. 2007.
15. N. Dobigeon, J.-Y. Tourneret, and J. D. Scargle, "Joint segmentation of multivariate astronomical time series: Bayesian sampling with a hierarchical model," IEEE Trans. Signal Process., vol. 55, no. 2, pp. 414-423, Feb. 2007.
16. A. Doucet and P. Duvaut, "Bayesian estimation of state-space models applied to deconvolution of Bernoulli-Gaussian processes," Signal Process., vol. 57, no. 2, pp. 147-161, Mar. 1997.
17. C. Févotte, B. Torrésani, L. Daudet, and S. J. Godsill, "Sparse linear regression with structured priors and application to denoising of musical audio," IEEE Trans. Audio, Speech, Lang. Process., vol. 16, no. 1, pp. 174-185, Jan. 2008.
18. J. Geweke, E. M. Keramidas, Ed., "Efficient simulation from the multivariate normal and student-T distributions subject to linear constraints," in Proc. 23rd Symp. Interface Computing Science and Statistics, Fairfax, VA, 1991, pp. 571-578.
19. S. J. Godsill and P. J. W. Rayner, "Statistical reconstruction and analysis of autoregressive signals in impulsive noise using the Gibbs sampler," IEEE Trans. Speech Audio Process., vol. 6, no. 4, pp. 352-372, Jul. 1998.
20. R. Gribonval and M. Nielsen, "Sparse representations in unions of bases," IEEE Trans. Inf. Theory, vol. 49, no. 12, pp. 3320-3325, Dec. 2003.
21. P. C. Hammel, D. V. Pelekhov, P. E. Wigen, T. R. Gosnell, M. M. Midzor, and M. L. Roukes, "The magnetic-resonance force microscope: A new tool for high-resolution, 3-D, subsurface scanned probe imaging," Proc. IEEE, vol. 91, no. 5, pp. 789-798, May 2003.
22. K. Herrity, R. Raich, and A. O. Hero, "Blind deconvolution for sparse molecular imaging," in Proc. IEEE Int. Conf. Acoust., Speech, and Signal Processing, Las Vegas, NV, Apr. 2008, pp. 545-548.
23. K. Herrity, R. Raich, and A. O. Hero, C. A. Bouman, E. L. Miller, and I. Pollak, Eds., "Blind reconstruction of sparse images with unknown point spread function," in Proc. Computational Imaging Conf. IS & TSPIE Symp. Electronic Imaging Science and Technology, San Jose, CA, USA, Jan. 2008, vol. 6814, pp. 68140K-1-68140K-11.
24. J. Idier and Y. Goussard, "Stack algorithm for recursive deconvolution of Bernoulli-Gaussian processes," IEEE Trans. Signal Process., vol. 28, no. 9, pp. 67-79, Sep. 1990.
25. H. Jeffreys, "An invariant form for the prior probability in estimation problems," Proc. Roy. Soc. Lond. A, vol. 186, no. 1007, pp. 453-461, 1946.
26. H. Jeffreys, Theory of Probability, 3rd ed. London, U.K.: Oxford Univ. Press, 1961.
27. I. M. Johnstone and B. W. Silverman, "Needles and straw in haystacks: Empirical Bayes estimates of possibly sparse sequences," Ann. Statist., vol. 32, no. 4, pp. 1594-1649, 2004.
28. J. J. Kormylo and J. M. Mendel, "Maximum likelihood detection and estimation of Bernoulli-Gaussian processes," IEEE Trans. Inf. Theory vol. 28, no. 3, pp. 482-488, May 1982.
29. S. Kuehn, S. A. Hickman, and J. A. Marohn, "Advances in mechanical detection of magnetic resonance," J. Chem. Phys., vol. 128, no. 5, pp. 052208-1-052208-19, Feb. 2008.
30. E. Kuhn and M. Lavielle, "Coupling a stochastic approximation version of EM with an MCMC procedure," ESAIM Probab. Statist., vol. 8, pp. 115-131, 2004.
31. L. Landweber, "An iteration formula for fredholm integral equations of the first kind," Amer. J. Math., vol. 73, no. 3, pp. 615-624, Jul. 1951.
32. M. Lavielle and E. Lebarbier, "An application of MCMC methods for the multiple change-points problem," Signal Process., vol. 81, no. 1, pp. 39-53, Jan. 2004.
33. M. Lavielle, "Bayesian deconvolution of Bernoulli-Gaussian processes," Signal Process., vol. 33, no. 1, pp. 67-79, Jul. 1993.
34. J. Mamin, R. Budakian, and D. Rugar, "Point response function of an MRFM tip," Tech. Rep., IBM Research Division, Oct. 2003.
35. J.-M. Marin and C. P. Robert, Bayesian Core: A Practical Approach to Computational Bayesian Statistics. New York, NY: Springer, 2007.
36. V. Mazet, D. Brie, and J. Idier, "Simulation of positive normal variables using several proposal distributions," in Proc. IEEE Workshop on Statistical Signal Processing (SSP), Bordeaux, France, Jul. 2005, pp. 37-42.
37. V. Mazet, "Développement De Méthodes De Traitement De Signaux Spectroscopiques: Estimation De La Ligne De Base Et Du Spectre De Raies," Ph.D. dissertation, Univ. Henri Poincaré, Nancy, France, 2006.
38. D. Mounce, "Magnetic resonance force microscopy," IEEE Instrum. Meas. Mag., vol. 8, no. 2, pp. 20-26, Jun. 2005.
39. T. Olofsson and E. Wennerström, "Sparse deconvolution of B-scan images," IEEE Trans. Ultrason. Ferroelectr. Freq. Control, vol. 54, no. 8, pp. 1634-1641, Aug. 2007.
40. E. Punskaya, C. Andrieu, A. Doucet, and W. Fitzgerald, "Bayesian curve fitting using MCMC with applications to signal segmentation," IEEE Trans. Signal Process., vol. 50, no. 3, pp. 747-758, Mar. 2002.
41. S. E. Reichenbach, D. E. Koehler, and D. W. Strelow, "Restoration and reconstruction of AVHRR images," IEEE Trans. Geosci. Remote Sens. vol. 33, no. 4, pp. 997-1007, Jul. 1995.
42. C. P. Robert, "Simulation of truncated normal variables," Statist. Comput., vol. 5, no. 2, pp. 121-125, Jun. 1995.
43. C. P. Robert, "The Bayesian choice: From decision-theoretic motivations to computational implementation," in Ser. Springer Texts in Statistics, 2nd ed. New York: Springer-Verlag, 2007.
44. C. P. Robert and G. Casella, Monte Carlo Statistical Methods, 2nd ed. New York: Springer, 2004.
45. O. Rosec, J.-M. Boucher, B. Nsiri, and T. Chonavel, "Blind marine seismic deconvolution using statistical MCMC methods," IEEE J. Ocean. Eng., vol. 28, no. 3, pp. 502-512, Jul. 2003.
46. D. Rugar, R. Budakian, H. J. Mamin, and B. W. Chui, "Single spin detection by magnetic resonance force microscopy," Nature, vol. 430, pp. 329-332, Jul. 2004.
47. J. C. Russ, The Image Processing Handbook, 5th ed. Boca Raton, FL: CRC, 2006.
48. P. Sarder and A. Nehorai, "Deconvolution methods for 3-D fluorescence microscopy images," IEEE Signal Process. Mag., vol. 23, no. 3, pp. 32-45, May 2006.
49. J.-L. Starck and F. Murtagh, Astronomical Image and Data Analysis, 2nd ed. Berlin, Germany: Springer-Verlag, 2006.
50. C. M. Stein, "Estimation of the mean of a multivariate normal distribution," Ann. Statist., vol. 9, no. 6, pp. 1135-1151, Nov. 1981.
51. R. Tibshirani, "Regression shrinkage and selection via the LASSO," J. Roy. Statist. Soc. B, vol. 58, no. 1, pp. 267-288, 1996.
52. M. Ting, R. Raich, and A. O. Hero, "Sparse image reconstruction using sparse priors," in Proc. IEEE Int. Conf. Image Processing, Oct. 2006, pp. 1261-1264.
53. M. Ting, R. Raich, and A. O. Hero, "Sparse image reconstruction for molecular imaging," IEEE Trans. Image Process., 2009.
54. M. Y. Ting, "Signal Processing for Magnetic Resonance Force Microscopy," Ph.D. dissertation, Univ. Michigan, Ann Arbor, 2006.
55. F. Sroubek and J. Flusser, "Multichannel blind iterative image restoration," IEEE Trans. Image Process., vol. 12, no. 9, pp. 1094-1106, Sep. 2003.
56. O. Züger, S. T. Hoen, C. S. Yannoni, and D. Rugar, "Three-dimensional imaging with a nuclear magnetic resonance force microscope," J. Appl. Phys., vol. 79, no. 4, pp. 1881-1884, Feb. 1996.
57. O. Züger and D. Rugar, "First images from a magnetic resonance force microscope," Appl. Phys. Lett., vol. 63, no. 18, pp. 2496-2498, 1993.
58. O. Züger and D. Rugar, "Magnetic resonance detection and imaging using force microscope techniques," J. Appl. Phys., vol. 75, no. 10, pp. 6211-6216, May 1994.