Bayesian sparsity estimation in compressive sensing with application to MR images

References

• Aubert-Broche, B., A. C. Evans, and L. Collins. 2006. “A New Improved Version of the Realistic Digital Brain Phantom.” NeuroImage 32 (1):138–45. doi: 10.1016/j.neuroimage.2006.03.052.
   PubMed Web of Science ®Google Scholar
• Besag, J., J. York, and A. Mollié. 1991. “Bayesian Image Restoration, with Two Applications in Spatial Statistics.” Annals of the Institute of Statistical Mathematics 43 (1):1–20. doi: 10.1007/BF00116466.
   Web of Science ®Google Scholar
• Braunisch, H., B.-I. Wu, and J. Kong. 2000. “Phase Unwrapping of SAR Interferograms after Wavelet Denoising.” IEEE Geoscience and Remote Sensing Symposium 2:752–4.
   Google Scholar
• Brynolfsson, P., J. Yu, R. Wirestam, M. Karlsson, and A. Garpebring. 2014. “Combining Phase and Magnitude Information for Contrast Agent Quantification in Dynamic Contrast-Enhanced MRI Using Statistical Modeling.” Magnetic Resonance in Medicine 74 (4):1156–64. doi: 10.1002/mrm.25490.
   PubMed Web of Science ®Google Scholar
• Candès, E. J., J. K. Romberg, and T. Tao. 2006. “Stable Signal Recovery from Incomplete and Inaccurate Measurements.” Communications on Pure and Applied Mathematics 59 (8):1207–23. doi: 10.1002/cpa.20124.
   Web of Science ®Google Scholar
• Cardin, M. 2009. “Multivariate Measures of Positive Dependence.” International Journal of Contemporary Mathematical Sciences 4 (4):191–200.
   Google Scholar
• Carroll, R., A. Lawson, C. Faes, R. Kirby, M. Aregay, and K. Watjou. 2015. “Comparing INLA and OpenBUGS for Hierarchical Poisson Modeling in Disease Mapping.” Spatial and Spatio-Temporal Epidemiology 14:45–54. doi: 10.1016/j.sste.2015.08.001.
   PubMed Web of Science ®Google Scholar
• Cressie, N. 1993. Statistics for Spatial Data. New York: Wiley.
   Google Scholar
• Cressie, N., and C. K. Wikle. 2011. Statistics for Spatio-Temporal Data. Hoboken, New Jersey: Wiley.
   Google Scholar
• Donoho, D. L. 1995. “De-noising by Soft-Thresholding.” IEEE Transactions on Information Theory 41 (3):613–27. doi: 10.1109/18.382009.
   Web of Science ®Google Scholar
• Donoho, D. L. 2006. “Compressed Sensing.” IEEE Transactions on Information Theory 52 (4):1289–306. doi: 10.1109/TIT.2006.871582.
   Web of Science ®Google Scholar
• Foucart, S., and H. Rauhut. 2013. A Mathematical Introduction to Compressive Sensing. New York: Springer.
   Google Scholar
• Haldar, J. P., D. Hernando, and Z.-P. Liang. 2010. “Compressed-Sensing MRI with Random Encoding.” IEEE Transactions on Medical Imaging 30 (4):893–903.
   PubMed Web of Science ®Google Scholar
• Harvey, D. J., Q. Weng, and L. A. Beckett. 2010. “On an Asymptotic Distribution of Dependent Random Variables on a 3-Dimensional Lattice.” Statistics & Probability Letters 80 (11–12):1015–21. doi: 10.1016/j.spl.2010.02.016.
   PubMed Web of Science ®Google Scholar
• Henkelman, R. M. 1985. “Measurement of Signal Intensities in the Presence of Noise in MR Images.” Medical Physics 12 (2):232–3. doi: 10.1118/1.595711.
   PubMed Web of Science ®Google Scholar
• Leroux, B. G., X. Lei, and N. Breslow. 2000. “Estimation of Disease Rates in Small Areas: A New Mixed Model for Spatial Dependence.” In Statistical Models in Epidemiology, the Environment, and Clinical Trials, edited by M. E. Halloran and D. Berry, 179–91. New York: Springer.
   Google Scholar
• Lindgren, F., H. Rue, and J. Lindström. 2011. “An Explicit Link between Gaussian Fields and Gaussian Markov Random Fields: The Stochastic Partial Differential Equation Approach.” Journal of the Royal Statistical Society: Series B (Statistical Methodology) 73 (4):423–98. doi: 10.1111/j.1467-9868.2011.00777.x.
   Web of Science ®Google Scholar
• Martino, S., and H. Rue. 2010. “Implementing Approximate Bayesian Inference for Latent Gaussian Models Using Integrated Nested Laplace Approximations: A Manual for the INLA-Program.” Department of Mathematical Sciences, Norwegian University of Science and Technology.
   Google Scholar
• Matérn, B. 1960. “Spatial Variation: Stochastic Models and Their Application to Some Problems in Forest Surveys and Other Sampling Investigations.” Diss., Statens skogsforskningsinstitut, Sthlm Univ.
   Google Scholar
• Prates, M. O., D. K. Dey, M. R. Willig, and J. Yan. 2015. “Transformed Gaussian Markov Random Fields and Spatial Modeling of Species Abundance.” Spatial Statistics 14:382–99. doi: 10.1016/j.spasta.2015.07.004.
   Web of Science ®Google Scholar
• Prinosil, J., Z. Smekal, and K. Bartusek. 2010. “Wavelet Thresholding Techniques in MRI Domain.” In Proceedings of IEEE International Conference on Biosciences, 58–63.
   Google Scholar
• Rue, H., and L. Held. 2005. Gaussian Markov Random Fields: Theory and Applications. Boca Raton: Chapman & Hall/CRC.
   Google Scholar
• Rue, H., S. Martino, and N. Chopin. 2009. “Approximate Bayesian Inference for Latent Gaussian Models by Using Integrated Nested Laplace Approximations.” Journal of the Royal Statistical Society: Series B (Statistical Methodology) 71 (2):319–92. doi: 10.1111/j.1467-9868.2008.00700.x.
   Web of Science ®Google Scholar
• Stein, M. L. 1999. Interpolation of Spatial Data. New York: Springer-Verlag.
   Google Scholar
• Vanithamani, R., and G. Umamaheswari. 2011. “Wavelet Based Despeckling of Medical Ultrasound Images with Bilateral Filter.” In TENCON 2011—2011 IEEE Region 10 Conference.
   Google Scholar
• Whittle, P. 1954. “On Stationary Processes in the Plane.” Biometrika 41 (3–4):434. doi: 10.1093/biomet/41.3-4.434.
   Web of Science ®Google Scholar
• Whittle, P. 1963. “Stochastic Processes in Several Dimensions.” Bulletin of the International Statistical Institute 40:974–94.
   Google Scholar