Iterative total least-squares image reconstruction algorithm for optical tomography by the conjugate gradient method

Journal of the Optical Society of America A: Optics and Image Science, and Vision

Volumn 14, Issue 4, 1997, Pages 799-807

  Zhu, Wenwu ^a,c   Wang, Yao ^a   Yao, Yuqi ^a,c   Chang, Jenghwa ^b   Graber, Harry L ^b  

^a POLYTECHNIC UNIVERSITY   (United States)

^b SUNY DOWNSTATE MEDICAL CENTER   (United States)

^c LUCENT TECHNOLOGIES   (United States)

Author keywords

Conjugate gradient method; Image reconstruction; Medical optical tomography; Total least squares

Indexed keywords

ALGORITHM; ARTICLE; COMPUTER SIMULATION; IMAGE PROCESSING; METHODOLOGY; OPHTHALMOLOGY; TOMOGRAPHY;

ALGORITHMS; COMPUTER SIMULATION; IMAGE PROCESSING, COMPUTER-ASSISTED; OPHTHALMOLOGY; TOMOGRAPHY;

ALGORITHMS; COMPUTER SIMULATION; GREEN'S FUNCTION; INTEGRODIFFERENTIAL EQUATIONS; ITERATIVE METHODS; LEAST SQUARES APPROXIMATIONS; MATHEMATICAL MODELS; MATRIX ALGEBRA; MEDICAL IMAGING; OPTICAL PROPERTIES; PERTURBATION TECHNIQUES; VECTORS;

CONJUGATE GRADIENT METHOD; DIFFUSION EQUATION; OPTICAL TOMOGRAPHY; RADIATION TRANSPORT EQUATION; TOTAL LEAST SQUARES;

IMAGE RECONSTRUCTION;

EID: 0031106975     PISSN: 10847529     EISSN: 15208532     Source Type: Journal    
DOI: 10.1364/JOSAA.14.000799     Document Type: Article

References (29)

1. R. L. Barbour, H. L. Graber, J. Chang, S. Barbour, P. C. Koo, and R. Aronson, “MR guided optical tomography: prospects and computation for a new imaging method,” in IEEE Computational Science Engineering Magazine, Winter 1995, pp. 63–77.
2. Y. Wang, J. Chang, R. Aronson, R. Barbour, H. Graber, and J. Lubowsky, “Imaging scattering media by diffusion tomography: an iterative perturbation approach,” in Physiological Monitoring and Early Detection Diagnostic Methods, T. S. Mang, ed., Proc. SPIE 1641, 58–71 (1992).
3. R. L. Barbour, H. L. Graber, Y. Wang, J. Chang, and R. Aronson, “A perturbation approach for optical diffusion tomography using continuous-wave and time-resolved data,” in Medical Optical Tomography: Functional Imaging and Monitoring, G. H. Mueller, B. Chance, R. R. Alfano, S. R. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. R. Masters, S. Svanberg, and P. van der Zee, eds., Vol. IS11 of Institute Series (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1993), pp. 87–120.
4. J. Chang, Y. Wang, R. Aronson, H. L. Graber, and R. L. Barbour, “A layer-stripping approach for recovery of scattering media from time-resolved data,” in Inverse Problems in Scattering and Imaging, M. A. Fiddy, ed., Proc. SPIE 1767, 384–395 (1992).
5. W. Zhu, Y. Wang, H. L. Graber, R. L. Barbour, and J. Chang, “A regularized progressive expansion algorithm for recovery of scattering media from time-resolved data,” in Advances in Optical Imaging and Photon Migration, R. R. Alfano, ed. (Optical Society of America, Washington, D.C., 1994), pp. 211–216.
6. W. Zhu, Y. Wang, Y. Deng, Y. Yao, and R. Barbour, “Multiresolution regularized least squares image reconstruction based on wavelet in optical tomography,” in Experimental and Numerical Methods for Solving Ill-Posed Inverse Problems: Medical and Nonmedical Applications, R. L. Barbour, M. J. Carvlin, and M. A. Fiddy, eds., Proc. SPIE 2570, 186–196 (1995).
7. S. R. Arridge, “The forward and inverse problems in time resolved infra-red imaging,” in Medical Optical Tomography: Functional Imaging and Monitoring, Vol. IS11 of Institute Series (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1993), pp. 35–64.
8. Y. Yao, Y. Wang, Y. Pei, W. Zhu, and R. L. Barbour, “Simultaneous reconstruction of absorption and scattering distributions in turbid media using a Born iterative method,” in Experimental and Numerical Methods for Solving Ill-Posed Inverse Problems: Medical and Nonmedical Applications, R. L. Barbour, M. J. Carvlin, and M. A. Fiddy, eds., Proc. SPIE 2570, 96–107 (1995).
9. H. Jiang, K. D. Paulsen, U. L. Osterberg, B. W. Pogue, and M. S. Patterson, “Optical image reconstruction using frequency domain data: simulations and experiments,” J.Opt. Soc. Am. A 13, 253–266 (1996).
10. H. L. Graber, R. L. Barbour, J. Chang, and R. Aronson, “Identification of the functional form of nonlinear effects of localized finite absorption in a diffusing medium,” in Optical Tomography; Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance and R. R. Alfano, eds., Proc. SPIE 2389, 669–681 (1995).
11. J. H. Justice and A. A. Vassiliou, “Diffraction tomography for geophysical monitoring of hydrocarbon reservoirs,” Proc. IEEE 78, 711–722 (1990).
12. V. Z. Mesarovic, N. P. Galatsanos, and A. Katsaggelos, “Regularized constrained total least squares image restoration,” IEEE Trans. Image Process. 4, 1096–1108 (1995).
13. P. Li, S. W. Flax, E. S. Ebbini, and M. O’Donnell, “Blocked element compensation in phased array imaging,” IEEE Trans. Ultrason. Frequencies Freq. Control 40, 282–292 (1993).
14. K. M. Case and P. F. Zweifel, Linear Transport Theory (Addison-Wesley, Reading, Mass., 1967), Chap. 8, pp. 194–231.
15. G. H. Golub and C. F. Van Loan, “An analysis of the total least squares problem,” SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal. 17, 883–893 (1980).
16. M. T. Silvia and E. C. Tacker, “Regularization of Marchenko’s integral equation by total least squares,” J. Acoust. Soc. Am. 72, 1202–1207 (1982).
17. G. H. Golub, “Some modified matrix eigenvalue problems,” SIAM Rev. 15, 318–334 (1973).
18. S. Van Huffel and J. Vandewalle, The Total Least Squares Problem: Computational Aspects and Analysis (SIAM Press, Philadelphia, 1991).
19. C. E. Davila, “An efficient recursive total least squares algorithm for FIR adaptive filtering,” IEEE Trans. Signal Process. 42, 268–280 (1994).
20. N. K. Bose, H. C. Kim, and H. M. Valenzuela, “Recursive total least squares algorithm for image reconstruction,” Multidimens. Syst. Signal Process. 4, 253–268 (1993).
21. H. Chen, T. K. Sarkar, S. A. Dianat, and J. D. Brule, “Adaptive spectral estimation by the conjugate gradient method,” IEEE Trans. Acoust. Speech Signal Process. ASSP-34, 272–284 (1986).
22. X. Yang, T. K. Sarkar, and E. Arvas, “A survey of conjugate gradient algorithms for solution of extreme eigen-problem of a symmetric matrix,” IEEE Trans. Acoust. Speech Signal Process. 37, 1550–1556 (1989).
23. I. Shavitt, C. F. Bender, A. Pipano, and R. P. Hosteny, “The iterative calculation of several of the lowest or highest eigenvalues and corresponding eigenvector of very large symmetric matrices,” J. Comput. Phys. 11, 90–108 (1973).
24. R. Fletcher and C. M. Reeves, “Function minimization by conjugate gradients,” Comput. J. 7, 149–154 (1964).
25. R. L. Barbour, H. L. Graber, R. Aronson, and J. Lubowsky, “Imaging of subsurface regions of random media by remote sensing,” in Time-Resolved Spectroscopy and Imaging of Tissues, B. Chance and A. Katzir, eds., Proc. SPIE 1431, 192–203 (1991).
26. Y. Q. Yao, Y. Wang, R. L. Barbour, H. L. Graber, and J. W. Chang, “Scattering characteristics of photon density waves from an object in a spherically two-layer medium,” in Optical Tomography, Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance and R. R. Alfano, eds., Proc. SPIE 2389, 291–303 (1995).
27. Y. Q. Yao, Y. Wang, Y. L. Pei, W. W. Zhu, J. H. Hu, and R. L. Barbour, “Frequency domain optical tomography in human tissue,” in Experimental and Numerical Methods for Solving Ill-Posed Inverse Problems: Medical and Nonmedical Applications, R. L. Barbour, M. J. Carvlin, and M. A. Fiddy, eds., Proc. SPIE 2570, 254–266 (1995).
28. W. Zhu, Y. Wang, Y. Yao, and R. L. Barbour, “Wavelet based multigrid reconstruction algorithm for optical tomography,” in Advances in Optical Imaging and Photon Migration, R. R. Alfano and J. Fujimoto, eds. (Optical Society of America, Washington, D.C., 1996), pp. 278–281.
29. T. J. Abatzoglou, J. M. Mendel, and G. A. Harada, “The constrained total least squares technique and its applications to harmonic superresolution,” IEEE Trans. Signal Process. 39, 1070–1087 (1991).