Abstract
Advances in medical imaging systems havemade significant contributions to medical diagnoses and treatments by providing anatomic and functional information about human bodies that is difficult to obtain without these techniques. These modalities also generate large quantities of noisy data that need modern techniques of computational statistics for image reconstruction, visualization and analysis. This article will report recent research in this area and suggest challenges that will need to be addressed by future studies. Specifically, I will discuss computational statistics for positron emission tomography, ultrasound images and magnetic resonance images from the perspectives of image reconstruction, image segmentation and vision model-based image analysis.
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References
Burckhardt, C.B. (1978). Speckle in ultrasound B-mode scans. IEEE Trans Ultrasonics, 25:1–6.
Censor, Y. (1983). Finite Series-Expansion Reconstruction Methods. Proc IEEE, 71:409–419.
Chatziioannou, A., Qi, J., Moore, A., Annala, A., Nguyen, K., Leahy, R. and Cherry, S. (2000). Comparison of 3D MAP and filtered backprojection algorithms for high resolution animal imaging with microPET. IEEE Trans Med Imaging, 19:507–512.
Chen, C.H. and Li, K.C. (1998). Can SIR be as popular as multiple linear regression? Stat Sinica, 8:289–316.
Chen, C.H. and Li, K.C. (2001). Generalization of Fisher’s linear discriminant analysis via the approach of sliced inverse regression. J Korean Stat Soc, 30:193–217.
Chen, C.M., Lu, H.H.S. and Lin, Y.C. (2000). An Early Vision Based Snake Model for Ultrasound Image Segmentation. Ultrasound Med Biol, 26:273–285.
Chen, C.M. and Lu, H.H.S. (2001). An Adaptive Snake Model for Ultrasound Image Segmentation: Modified Trimmed Mean Filter, Ramp Integration and Adaptive Weighting Parameters. Ultrason Imag, 22:214–236.
Chen, C.M., Lu, H.H.S. and Han, K.C. (2001). A Textural Approach Based on Gabor Functions for Texture Edge Detection in Ultrasound Images. Ultrasound Med Biol, 27:513–534.
Chen, C.M., Lu, H.H.S. and Hsiao, A.T. (2001). A Dual Snake Model of High Penetrability for Ultrasound Image Boundary Extraction. Ultrasound Med Biol, 27:1651–1665.
Chen, C.M., Lu, H.H.S. and Huang, Y.S. (2002). Cell-Based Dual Snake Model: A New Approach to Extracting Highly Winding Boundaries in The Ultrasound Images. Ultrasound Med Biol, 28:1061–1073.
Chen, C.M., Lu, H.H.S. and Chen, Y.L. (2003). A Discrete Region Competition Approach Incorporating Weak Edge Enhancement for Ultrasound Image Segmentation. Pattern Recogn Lett, 24:693–704.
Chen, T.B., Chen, J.C., Lu, H.H.S. and Liu, R.S. (2007). MicroPET Reconstruction with Random Coincidence Correction via a Joint Poisson Model. Medical Engineering & Physics, (in press).
Dunn, D., Higgins, W.E. and Wakeley, J. (1994). Texture segmentation using 2-D Gabor elementary functions. IEEE Trans Pattern Anal Mach Intell, 16:130–149.
Fessler, J.A. (1994). Penalized Weighted Least-Squares Image Reconstruction for Positron Emission Tomography. IEEE Trans Med Imag, 13:292–300.
Fessler, J.A. and Hero, A.O. (1994). Space-alternating generalized expectation-maximization algorithm. IEEE Trans Signal Proc, 42:2664–2677.
Fessler, J.A. and Hero, A.O. (1995). Penalized maximum-likelihood image reconstruction using space-alternating generalized expectation-maximization algorithms. IEEE Trans Imag Process, 4:1417–1429.
Goodman, J.W. (1985). Statistical Optics. Wiley, New York.
Herman, G.T. (1980). Image Reconstruction From Projections: The Fundamentals of Computerized Tomography. Academic, New York.
Herman, G.T., Lent, A. and Hurwitz, H. (1980). A Storage-Efficient Algorithm for Finding the Regularized Solution of a Large Inconsistent system of Equations. J Inst Math Applic, 25:361–366.
Jain, A.K. and Farrokhnia, F. (1991). Unsupervised texture segmentation using Gabor filters. Pattern Recogn, 24:1167–1186.
Kevles, B.H. (1997). Naked to the Bone: Medical Imaging in the Twentieth Century. Rutgers University Press, Piscataway, NJ.
Li, K.C. (1991). Sliced inverse regression for dimensional reduction (with discussion). J Am Stat Assoc, 86:316–342.
Li, K.C. (2000). High dimensional data analysis via the SIR/PHD approach. Lecture Notes, Department of Statistics, UCLA, Los Angeles, CA (http://www.stat.ucla.edu/∼ kcli/sir-PHD.pdf).
Lu, H.H.S., Chen, C.M. and Yang, I.H. (1998). Cross-Reference Weighted Least Square Estimates for Positron Emission Tomography. IEEE Trans Med Imag, 17:1–8.
Lu, H.H.S. and Tseng, W.J. (1997). On Accelerated Cross-Reference Maximum Likelihood Estimates for Positron Emission Tomography. Proc IEEE Nucl Sci Symp, 2:1484–1488.
Malik, J. and Perona, P. (1990). Preattentive texture discrimination with early vision mechanisms. J Opt Soc Am A, 7:923–932.
Meng, X.L. and Rubin, D.B. (1993). Maximum likelihood estimation via the ECM algorithm: A general framework. Biometrika, 80:267–278.
Ouyang, X., Wong, W.H., Johnson, V.E., Hu, X. and Chen, C.T. (1994). Incorporation of Correlated Structural Images in PET Image Reconstruction. IEEE Trans Med Imag, 13:627–640.
Politte, F.G. and Snyder, D.L. (1991). Corrections for Accidental Coincidences and Attenuation in Maximum-Likelihood Image Reconstruction for Positron-Emission Tomography. IEEE Trans Med Imag, 10:82–89.
Prince, J.L. and Links, J. (2005). Medical Imaging Signals and Systems. Prentice Hall, Upper Saddle River, NJ.
Shepp, L.A. and Vardi, Y. (1982). Maximum Likelihood Reconstruction for Emission Tomography. IEEE Trans Med Imag, 1:113–122.
Soatto, S., Doretto, G. and Wu, Y. (2001). Dynamic textures. Intl Conf Comput Vis, 439–446.
Spinks, T.J., Jones, T., Gilardi, M.C. and Heather, J.D. (1988). Physical Performance of the Latest Generation of Commercial Positron Scanner. IEEE Trans Nucl Sci, 35:721–725.
Suetens, P. (2002). Fundamentals of Medical Imaging. Cambridge University Press, Cambridge.
Tan, T.N. (1995). Texture edge detection by modelling visual cortical channels. Pattern Recogn, 28:1283–1298.
Tu, K.Y., Chen, T.B., Lu, H.H.S., Liu, R.S., Chen, K.L., Chen, C.M. and Chen, J.C. (2001). Empirical Studies of Cross-Reference Maximum Likelihood Estimate Reconstruction for Positron Emission Tomography. Biomed Eng – Appl Basis Commun, 13:1–7.
Vardi, Y., Shepp, L.A. and Kaufman, L. (1985). A Statistical Model for Positron Emission Tomography. J Am Stat Assoc, 80:8–20.
Weaver, H.J. (1983). Applications of Discrete and Continuous Fourier Analysis. Wiley, New York.
Wu, H.M. and Lu, H.H.S. (2004). Supervised motion segementation by spatial-frequential analysis and dynamic sliced inverse regression. Stat Sinica, 14:413–430.
Wu, Y., Zhu, S.C. and Guo, C. (2002). Statistical modelling of texture sketch. Proc Eur Conf Comp Vis, 240–254.
Wu, Y., Zhu, S.C. and Liu, X. (2000). Equivalence of Julesz texture ensembles and FRAME models. Int J Comp Vis, 38:247–265.
Xiang, D. and Wahba, G. (1996). A generalized approximate cross validation for smoothing splines with non-Gaussian data. Stat Sinica, 6:675–692.
Zhu, S.C., Liu, X. and Wu, Y. (2000). Exploring texture ensembles by efficient Markov Chain Monte Carlo – towards a ‘Trichromacy’ theory of texture. IEEE Trans Pattern Anal Mach Intell, 22:554–569.
Zhu, S.C., Wu, Y. and Mumford, D.B. (1998). Filter, random field, and maximum entropy (FRAME): towards a unified theory for texture modelling. Int J Comp Vis, 27:107–126.
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Lu, HS. (2008). Reconstruction, Visualization and Analysis of Medical Images. In: Handbook of Data Visualization. Springer Handbooks Comp.Statistics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-33037-0_31
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DOI: https://doi.org/10.1007/978-3-540-33037-0_31
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