## Total variation regularization for nonlinear fluorescence tomography with an augmented Lagrangian splitting approach

Applied Optics, Vol. 49, Issue 19, pp. 3741-3747 (2010)

http://dx.doi.org/10.1364/AO.49.003741

Enhanced HTML Acrobat PDF (480 KB)

### Abstract

Fluorescence tomography is an imaging modality that seeks to reconstruct the distribution of fluorescent dyes inside a highly scattering sample from light measurements on the boundary. Using common inversion methods with

© 2010 Optical Society of America

**OCIS Codes**

(100.3190) Image processing : Inverse problems

(100.6950) Image processing : Tomographic image processing

(170.3660) Medical optics and biotechnology : Light propagation in tissues

(260.2510) Physical optics : Fluorescence

**ToC Category:**

Image Processing

**History**

Original Manuscript: January 12, 2010

Manuscript Accepted: May 25, 2010

Published: June 24, 2010

**Virtual Issues**

Vol. 5, Iss. 11 *Virtual Journal for Biomedical Optics*

**Citation**

Manuel Freiberger, Christian Clason, and Hermann Scharfetter, "Total variation regularization for nonlinear fluorescence tomography with an augmented Lagrangian splitting approach," Appl. Opt. **49**, 3741-3747 (2010)

http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=ao-49-19-3741

Sort: Year | Journal | Reset

### References

- J. S. Reynolds, T. L. Troy, and E. M. Sevick-Muraca, “Multipixel techniques for frequency-domain photon migration imaging,” Biotechnol. Prog. 13, 669–680 (1997). [CrossRef] [PubMed]
- A. B. Milstein, S. Oh, K. J. Webb, C. A. Bouman, Q. Zhang, D. A. Boas, and R. P. Millane, “Fluorescence optical diffusion tomography,” Appl. Opt. 42, 3081–3094 (2003). [CrossRef] [PubMed]
- D. S. Elson, I. Munro, J. Requejo-Isidro, J. McGinty, C. Dunsby, N. Galletly, G. W. Stamp, M. A. A. Neil, M. J. Lever, P. A. Kellett, A. Dymoke-Bradshaw, J. Hares, and P. M. W. French, “Real-time time-domain fluorescence lifetime imaging including single-shot acquisition with a segmented optical image intensifier,” New J. Phys. 6, 180 (2004). [CrossRef]
- I. S. Longmuir and J. A. Knopp, “Measurement of tissue oxygen with a fluorescent probe,” J. Appl. Physiol. 41, 598–602(1976). [PubMed]
- E. Shives, Y. Xu, and H. Jiang, “Fluorescence lifetime tomography of turbid media based on an oxygen-sensitive dye,” Opt. Express 10, 1557–1562 (2002). [PubMed]
- Y. Y. Chen and A. W. Wood, “Application of a temperature-dependent fluorescent dye (Rhodamine B) to the measurement of radiofrequency radiation-induced temperature changes in biological samples,” Bioelectromagnetics (N.Y.) 30, 583–590 (2009). [CrossRef]
- S. Mordon, V. Maunoury, J. M. Devoisselle, Y. Abbas, and D. Coustaud, “Characterization of tumorous and normal tissue using a pH-sensitive fluorescence indicator (5,6-carboxyfluorescein) in vivo,” J. Photochem. Photobiol. B 13, 307–314(1992). [CrossRef] [PubMed]
- I. Gannot, I. Ron, F. Hekmat, V. Chernomordik, and A. Gandjbakhche, “Functional optical detection based on pH dependent fluorescence lifetime,” Lasers Surg. Med. 35, 342–348 (2004). [CrossRef] [PubMed]
- M. A. O’Leary, D. A. Boas, X. D. Li, B. Chance, and Y. G. Yodh, “Fluorescence lifetime imaging in turbid media,” Opt. Lett. 21, 158–160 (1996). [CrossRef] [PubMed]
- V. Ntziachristos and R. Weissleder, “Experimental three-dimensional fluorescence reconstruction of diffuse media by use of a normalized born approximation,” Opt. Lett. 26, 893–895 (2001). [CrossRef]
- A. Joshi, W. Bangerth, and W. M. Sevick-Muraca, “Adaptive finite element based tomography for fluorescence optical imaging in tissue,” Opt. Express 12, 5402–5417 (2004). [CrossRef] [PubMed]
- S. R. Arridge, “Optical tomography in medical imaging,” Inverse Probl. 15, R41–R93 (1999). [CrossRef]
- A. Joshi, “Adaptive finite element methods for fluorescence enhanced optical tomography,” Ph.D. dissertation (Texas A&M University2005).
- H. Egger, M. Freiberger, and M. Schlottbom, “Analysis of forward and inverse models in fluorescence optical tomography,” Tech. Rep. SFB-2009-075 (SFB Research Center “Mathematical Optimization and Applications in Biomedical Sciences,” 2009).
- A. B. Bakushinsky and M. Y. Kokurin, Iterative Methods for Approximate Solution of Inverse Problems, Vol. 577 of Mathematics and Its Applications (Springer, 2004).
- H. W. Engl, M. Hanke, and A. Neubauer, Regularization of Inverse Problems (Kluwer, 1996). [CrossRef]
- B. Blaschke, A. Neubauer, and O. Scherzer, “On convergence rates for the iteratively regularized Gauss-Newton method,” IMA J. Numer. Anal. 17, 421–436 (1997). [CrossRef]
- T. Hohage, “Logarithmic convergence rates of the iteratively regularized Gauss-Newton method for an inverse potential and an inverse scattering problem,” Inverse Probl. 13, 1279–1299 (1997). [CrossRef]
- A. Chambolle, “An algorithm for total variation minimization and applications,” J. Math. Imaging Vision 20, 73 (2004). [CrossRef]
- A. Chambolle, “Total variation minimization and a class of binary MRF models,” in Proceedings of International Workshop on Energy Minimization Methods in Computer Vision and Pattern Recognition (2005), pp. 136–152. [CrossRef]
- M. R. Hestenes, “Multiplier and gradient methods,” J. Optimization Theory Appl. 4, 303–320 (1969). [CrossRef]
- M. J. D. Powell, “A method for nonlinear constraints in minimization problems,” in Optimization (Academic, 1969), pp. 283–298.
- R. Glowinski and A. Marrocco, “Sur l’approximation, par éléments finis d’ordre 1, et la résolution, par pénalisation-dualité, d’une classe de problèmes de Dirichlet non linéaires,” C. R. Acad. Sci. Paris Ser. A 278, 1649–1652 (1974).
- D. Gabay and B. Mercier, “A dual algorithm for the solution of nonlinear variational problems via finite element approximation,” Comput. Math. Appl. 2, 17–40 (1976). [CrossRef]
- R. Glowinski, Numerical Methods for Nonlinear Variational Problems, Scientific Computation (Springer-Verlag, 2008). Reprint of the 1984 original.
- T. Goldstein and S. Osher, “The split Bregman method for L1-regularized problems,” SIAM J. Imaging Sci. 2, 323–343(2009). [CrossRef]
- C. Clason, B. Jin, and K. Kunisch, “A duality-based splitting method for ℓ1-TV image restoration with automatic regularization parameter choice,” SIAM J. Sci. Comput. 32, 1484–1505 (2010). [CrossRef]
- M. Tao and J. Yang, “Alternating direction algorithms for total variation deconvolution in image reconstruction,” TR0918, Department of Mathematics, Nanjing University, 2009.
- Y. Nesterov, “Smooth minimization of non-smooth functions,” Math. Program. 103, 127–152 (2005). [CrossRef]
- P. Weiss, L. Blanc-Féraud, and G. Aubert, “Efficient schemes for total variation minimization under constraints in image processing,” SIAM J. Sci. Comput. 31, 2047–2080 (2009). [CrossRef]
- J.-F. Aujol, “Some first-order algorithms for total variation based image restoration,” J. Math. Imaging Vision 34, 307–327 (2009). [CrossRef]
- I. Ekeland and R. Témam, Convex Analysis and Variational Problems (Society for Industrial and Applied Mathematics, 1999). [CrossRef]
- G. Alexandrakis, F. R. Rannou, and A. F. Chatziioannou, “Tomographic bioluminescence imaging by use of a combined optical-pet (opet) system: a computer simulation feasibility study,” Phys. Med. Biol. 50, 4225–4241 (2005). [CrossRef] [PubMed]
- M. Keijzer, W. M. Star, and P. R. M. Storchi, “Optical diffusion in layered media,” Appl. Opt. 27, 1820–1824 (1988). [CrossRef] [PubMed]
- V. A. Morozov, “On the solution of functional equations by the method of regularization,” Sov. Math. Dokl. 7, 414–417(1966).
- M. Hintermüller and K. Kunisch, “Path-following methods for a class of constrained minimization problems in function space,” SIAM J. Optim. 17, 159–187 (2006). [CrossRef]
- G. Stadler, “Path-following and augmented Lagrangian methods for contact problems in linear elasticity,” J. Comput. Appl. Math. 203, 533–547 (2007). [CrossRef]
- K. Ito and K. Kunisch, “On the choice of the regularization parameter in nonlinear inverse problems,” SIAM J. Optim. 2, 376–404 (1992). [CrossRef]
- K. Kunisch and J. Zou, “Iterative choices of regularization parameters in linear inverse problems,” Inverse Probl. 14, 1247–1264 (1998). [CrossRef]
- C. Clason, B. Jin, and K. Kunisch, “A semismooth Newton method for L1 data fitting with automatic choice of regularization parameters and noise calibration,” SIAM J. Imaging Sci. 3, 199–231 (2010). [CrossRef]
- T. Pock, M. Unger, D. Cremers, and H. Bischof, “Fast and exact solution of total variation models on the GPU,” in IEEE Computer Society Conference on Computer Vision and Pattern Recognition Workshops, 2008. CVPRW ’08 (2008), pp. 1–8. [CrossRef]

## Cited By |
Alert me when this paper is cited |

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article | Next Article »

OSA is a member of CrossRef.