SPIRAL out of convexity: Sparsity-regularized algorithms for photon-limited imaging

Proceedings of SPIE - The International Society for Optical Engineering

Volumn 7533, Issue , 2010, Pages

  Harmany, Zachary T ^a   Marcia, Roummel F ^b   Willett, Rebecca M ^a  

^a Duke University   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Compressed sensing; Optimization; Poisson intensity; Recursive dyadic partitions; Wavelets

Indexed keywords

COMPRESSED SENSING; COMPUTATIONALLY EFFICIENT; DISCRETE EVENTS; DISTRIBUTED PHENOMENA; GAUSSIAN NOISE MODEL; LOG LIKELIHOOD; MULTISCALE ESTIMATION; NONNEGATIVITY CONSTRAINTS; OBJECTIVE FUNCTIONS; OPTIMIZATION FORMULATIONS; PHOTON-LIMITED IMAGING; POISSON DATA; POISSON NOISE; SEPARABLE APPROXIMATION; SPARSE REPRESENTATION;

INVERSE PROBLEMS; PHOTONS; SIGNAL RECONSTRUCTION;

OPTIMIZATION;

EID: 77952025447     PISSN: 0277786X     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1117/12.850771     Document Type: Conference Paper

References (31)

1. D. Snyder, Random Point Processes, Wiley-Interscience, New York, NY, 1975.
2. E. J. Candès and T. Tao, "Decoding by linear programming," IEEE Trans. Inform. Theory 15, pp. 4203-4215, December 2005.
3. D. Donoho, "Compressed sensing," IEEE Trans. Inform. Theory 52, pp. 1289-1306, April 2006.
4. E. Candès, J. Romberg, and T. Tao, "Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information," IEEE Transactions on Information Theory 52(2), pp. 489 - 509, 2006.
5. E. J. Candès and T. Tao, "Near-optimal signal recovery from random projections: universal encoding strategies?," IEEE Trans. Inform. Theory 52, pp. 5406-5425, December 2006.
6. R. Willett and M. Raginsky, "Performance bounds for compressed sensing with Poisson noise," in Proc. of IEEE Int. Symp. on Inf. Theory, 2009.
7. M. Raginsky, Z. T. Harmany, R. F. Marcia, and R.Willett, "Performance bounds for compressed sensing with Poisson noise," IEEE Trans. on Signal Proc. , 2009. Submitted.
8. D. Lingenfelter, J. Fessler, and Z. He, "Sparsity regularization for image reconstruction with Poisson data," in Proc. SPIE Computational Imaging VII, 7246, 2009.
9. J. A. Tropp, "Just relax: convex programming methods for identifying sparse signals in noise," IEEE Trans. Inform. Theory 52, pp. 1030-1051, March 2006.
10. R. Tibshirani, "Regression shrinkage and selection via the lasso," J. Roy. Statist. Soc. Ser. B 58(1), pp. 267-288, 1996.
11. S. Ahn and J. Fessler, "Globally convergent image reconstruction for emission tomography using relaxed ordered subsets algorithms," IEEE Trans. Med. Imaging 22, pp. 613-626, May 2003.
12. A. Dempster, N. Laird, and D. Rubin, "Maximum likelihood from incomplete data via the EM algorithm," Royal statistical Society B 39, pp. 1-38, 1977.
13. Y. Vardi, L. Shepp, and L. Kaufman, "A statistical model for positron emission tomography," Journal of the American Statistical Association 80, No.389, pp. 8-20, 1985.
14. J.-L. Starck and J. Bobin, "Astronomical data analysis and sparsity: from wavelets to compressed sensing," Proc. IEEE: Special Issue on Applications of Sparse Representation and Compressive Sensing , 2010. In press.
15. E. Kolaczyk, "Wavelet shrinkage estimation of certain poisson intensity signals using corrected thresholds," Statistica Sinica 9, pp. 119-135, 1999.
16. E. Kolaczyk and R. Nowak, "Multiscale likelihood analysis and complexity penalized estimation," Ann. Statist. 32, pp. 500-527, 2004. (Pubitemid 41250303)
17. R. Nowak and E. Kolaczyk, "A multiscale statistical framework for Poisson inverse problems," IEEE Trans. Info. Theory 46, pp. 1811-1825, 2000.
18. K. Timmermann and R. Nowak, "Multiscale modeling and estimation of Poisson processes with application to photon-limited imaging," IEEE Transactions on Information Theory 45(3), pp. 846-862, 1999.
19. R. Willett and R. Nowak, "Platelets: a multiscale approach for recovering edges and surfaces in photon-limited medical imaging," IEEE Transactions on Medical Imaging 22(3), pp. 332-350, 2003.
20. J. Liu and P. Moulin, "Complexity-regularized denoising of Poisson-corrupted data," in Proc. Intl. Conf. on Image Processing, 3, pp. 254-257, 2000.
21. J. A. Fessler and H. Erdoǧan, "A paraboloidal surrogates algorithm for convergent penalized-likelihood emission image reconstruction," in Proc. IEEE Nuc. Sci. Symp. Med. Im. Conf., 1998.
22. Z. Harmany, R. Marcia, and R. Willett, "Sparse Poisson intensity reconstruction algorithms," in IEEE Workshop on Statistical Signal Processing, 2009. Available at http://arxiv.org/abs/0905.0483.
23. D. R. Hunter and K. Lange, "A tutorial on MM algorithms," The American Statistician 58, pp. 30-37, 2004.
24. S. Wright, R. Nowak, and M. Figueiredo, "Sparse reconstruction by separable approximation," IEEE Trans. Signal Process. , 2009 (to appear).
25. J. Barzilai and J. M. Borwein, "Two-point step size gradient methods," IMA J Numer Anal 8(1), pp. 141-148, 1988.
26. M. A. T. Figueiredo, R. D. Nowak, and S. J. Wright, "Gradient projection for sparse reconstruction: Application to compressed sensing and other inverse problems," IEEE Trans. Sel. Top. Signal Process. 1(4), pp. 586-597, 2007.
27. S. Boyd and L. Vandenberghe, Convex Optimization, Cambridge University Press, Cambridge, 2004.
28. R. Willett and R. Nowak, "Multiscale Poisson intensity and density estimation," IEEE Trans. Inform. Theory 53(9), pp. 3171-3187, 2007.
29. R. Baraniuk, V. Cevher, M. Duarte, and C. Hegde, "Model-based compressive sensing," IEEE Trans. on Inform. Theory , 2008. Submitted.
30. J. A. Fessler and A. O. Hero, "Penalized maximum-likelihood image reconstruction using space-alternating generalized EM algorithms," IEEE Trans. Im. Proc. 4(10), pp. 1417-1429, 1995.
31. J. A. Fessler et al., "Image reconstruction toolbox." http://www.eecs.umich.edu/~fessler/code.