Search search
submit Submit
Publication Date
to
Vol. 133
Latest Volume
All Volumes
PIER 180 [2024] PIER 179 [2024] PIER 178 [2023] PIER 177 [2023] PIER 176 [2023] PIER 175 [2022] PIER 174 [2022] PIER 173 [2022] PIER 172 [2021] PIER 171 [2021] PIER 170 [2021] PIER 169 [2020] PIER 168 [2020] PIER 167 [2020] PIER 166 [2019] PIER 165 [2019] PIER 164 [2019] PIER 163 [2018] PIER 162 [2018] PIER 161 [2018] PIER 160 [2017] PIER 159 [2017] PIER 158 [2017] PIER 157 [2016] PIER 156 [2016] PIER 155 [2016] PIER 154 [2015] PIER 153 [2015] PIER 152 [2015] PIER 151 [2015] PIER 150 [2015] PIER 149 [2014] PIER 148 [2014] PIER 147 [2014] PIER 146 [2014] PIER 145 [2014] PIER 144 [2014] PIER 143 [2013] PIER 142 [2013] PIER 141 [2013] PIER 140 [2013] PIER 139 [2013] PIER 138 [2013] PIER 137 [2013] PIER 136 [2013] PIER 135 [2013] PIER 134 [2013] PIER 133 [2013] PIER 132 [2012] PIER 131 [2012] PIER 130 [2012] PIER 129 [2012] PIER 128 [2012] PIER 127 [2012] PIER 126 [2012] PIER 125 [2012] PIER 124 [2012] PIER 123 [2012] PIER 122 [2012] PIER 121 [2011] PIER 120 [2011] PIER 119 [2011] PIER 118 [2011] PIER 117 [2011] PIER 116 [2011] PIER 115 [2011] PIER 114 [2011] PIER 113 [2011] PIER 112 [2011] PIER 111 [2011] PIER 110 [2010] PIER 109 [2010] PIER 108 [2010] PIER 107 [2010] PIER 106 [2010] PIER 105 [2010] PIER 104 [2010] PIER 103 [2010] PIER 102 [2010] PIER 101 [2010] PIER 100 [2010] PIER 99 [2009] PIER 98 [2009] PIER 97 [2009] PIER 96 [2009] PIER 95 [2009] PIER 94 [2009] PIER 93 [2009] PIER 92 [2009] PIER 91 [2009] PIER 90 [2009] PIER 89 [2009] PIER 88 [2008] PIER 87 [2008] PIER 86 [2008] PIER 85 [2008] PIER 84 [2008] PIER 83 [2008] PIER 82 [2008] PIER 81 [2008] PIER 80 [2008] PIER 79 [2008] PIER 78 [2008] PIER 77 [2007] PIER 76 [2007] PIER 75 [2007] PIER 74 [2007] PIER 73 [2007] PIER 72 [2007] PIER 71 [2007] PIER 70 [2007] PIER 69 [2007] PIER 68 [2007] PIER 67 [2007] PIER 66 [2006] PIER 65 [2006] PIER 64 [2006] PIER 63 [2006] PIER 62 [2006] PIER 61 [2006] PIER 60 [2006] PIER 59 [2006] PIER 58 [2006] PIER 57 [2006] PIER 56 [2006] PIER 55 [2005] PIER 54 [2005] PIER 53 [2005] PIER 52 [2005] PIER 51 [2005] PIER 50 [2005] PIER 49 [2004] PIER 48 [2004] PIER 47 [2004] PIER 46 [2004] PIER 45 [2004] PIER 44 [2004] PIER 43 [2003] PIER 42 [2003] PIER 41 [2003] PIER 40 [2003] PIER 39 [2003] PIER 38 [2002] PIER 37 [2002] PIER 36 [2002] PIER 35 [2002] PIER 34 [2001] PIER 33 [2001] PIER 32 [2001] PIER 31 [2001] PIER 30 [2001] PIER 29 [2000] PIER 28 [2000] PIER 27 [2000] PIER 26 [2000] PIER 25 [2000] PIER 24 [1999] PIER 23 [1999] PIER 22 [1999] PIER 21 [1999] PIER 20 [1998] PIER 19 [1998] PIER 18 [1998] PIER 17 [1997] PIER 16 [1997] PIER 15 [1997] PIER 14 [1996] PIER 13 [1996] PIER 12 [1996] PIER 11 [1995] PIER 10 [1995] PIER 09 [1994] PIER 08 [1994] PIER 07 [1993] PIER 06 [1992] PIER 05 [1991] PIER 04 [1991] PIER 03 [1990] PIER 02 [1990] PIER 01 [1989]
All Journals
PIER PIER B PIER C PIER M PIER Letters
2012-10-19
The Sparsity-Promoted Solution to the Undersampling Tof-PET Imaging: Numerical Simulations
By
Dapeng Lao,

    Dr. Dapeng Lao

    Department of Petroleum Engineering

    Texas A&M University

    USA

    Homepage

Mark W. Lenox,

    Dr. Mark W. Lenox

    Texas A&M Institute for Preclinical Studies

    Texas A&M University

    USA

    Homepage

Gamal Akabani

    Dr. Gamal Akabani

    Department of Nuclear Engineering

    Texas A&M University

    Homepage

Progress In Electromagnetics Research, Vol. 133, 235-258, 2013
doi:10.2528/PIER12080711
Abstract
Recently, the limited-angle TOF-PET system has become an active research topic due to the considerable reduction of hardware cost and potential applicability for performing needle biopsy on patients while in the scanner. This undersampling measurement configuration oftentimes suffers from the deteriorated reconstructed images. However, the established theory of Compressed Sampling (CS) provides a potential framework for undertaking this problem, given that the imaged object can be sparse in some transformed domain. In here, we studied using numerical simulations the application of sparsity-promoted framework to TOF-PET imaging for two undersampling configurations. From these simulations, a relationship was obtained between the number of detectors (or the range of angle) and TOF time resolution, which provided an empirical guide of designing a low-cost TOF-PET systems while ensuring good reconstruction quality. Another contribution is the exploration of p-TV regularization, which showed that RMSE (Root of Mean Square Error) and SSIM (Structural Similarity) were optimized when p = 0.5. Several sets of representative numerical experiments were executed to validate the proposed methodology, which demonstrates the promising applicability of undersampling TOF-PET imaging.
Citation
Dapeng Lao, Mark W. Lenox, and Gamal Akabani, "The Sparsity-Promoted Solution to the Undersampling Tof-PET Imaging: Numerical Simulations," Progress In Electromagnetics Research, Vol. 133, 235-258, 2013.
doi:10.2528/PIER12080711
References

1. Jamieson, D. G. and J. H. Greenberg, "Positron emission tomography of the brain," Computerized Medical Imaging and Graphics, Vol. 13, No. 1, 61-79, 1989.
doi:10.1016/0895-6111(89)90079-7

2. Ollinger, J. M. and J. A. Fessler, "Positron-emission tomography," IEEE Signal Processing Magazine, Vol. 14, No. 1, 43-55, 1997.
doi:10.1109/79.560323

3. Conti, M., et al. "First experimental results of time-of-flight reconstruction on an LSO PET scanner," Physics in Medicine and Biology, Vol. 50, 4507-4526, 2005.
doi:10.1088/0031-9155/50/19/006

4. Muehllehner, G. and J. S. Karp, "Positron emission tomography," Physics in Medicine and Biology, Vol. 51, R117-R137, 2006.
doi:10.1088/0031-9155/51/13/R08

5. Surti, S. and J. S. Karp, "Design considerations for a limited angle, dedicated breast, TOF PET scanner," Physics in Medicine and Biology, Vol. 53, 2911-2921, 2008.
doi:10.1088/0031-9155/53/11/010

6. Mallat, S., A Wavelet Tour of Signal Processing, Academic-Press, 1998.

7. Aharon, M., M. Elad, and A. Bruckstein, "K-SVD: An algorithm for designing overcomplete dictionaries for sparse representation," IEEE Trans. Signal Prcoessing, Vol. 54, 4311, Nov. 2006.
doi:10.1109/TSP.2006.881199

8. Lee, K., S. Tak, and J. Ye, "A data-driven sparse GLM for fMRI analysis using sparse dictionary learning with MDL criterion," IEEE Trans. Medical Imaging, Vol. 30, 1076-1089, May 2011.

9. Ravishankar, S. and Y. Bresler, "MR image reconsruction from highly undersampled K-space data by dictionary learning," IEEE Trans. Medical Imaging, Vol. 30, 1028-1041, 2011.
doi:10.1109/TMI.2010.2090538

10. Bouman, C. and K. Sauer, "A generalized Gaussian image model for edge-perserving map estimation," IEEE Trans. Signal Processing, Vol. 2, 296-310, Jul. 1993.

11. Rudin, L., S. Osher, and E. Fatemi, "Nonlinear total variation based noise removal algorithms," Physics D, Vol. 60, 259-268, Jul. 1992.
doi:10.1016/0167-2789(92)90242-F

12. Unser, M. and P. Tafti, "Stochastic models for sparse and piecewise-smooth processing," IEEE Trans. Signal Processing, Vol. 59, 989-1006, Mar. 2011.
doi:10.1109/TSP.2010.2091638

13. Karahanoglu, F., I. Bayram, and D. van de Ville, "A signal processing approach to generalized 1-D total variation," IEEE Trans. Signal Processing, Vol. 59, 5265-5274, Nov. 2011.
doi:10.1109/TSP.2011.2164399

14. Rodriguez, P. and B. Wohlberg, "Efficient minimization method for a generalized total variation functional," IEEE Trans. Image Processing, Vol. 18, 322-332, Feb. 2009.
doi:10.1109/TIP.2008.2008420

15. Candes, E., J. Romberg, and T. Tao, "Stable signal recovery from incomplete and inaccurate measurements," Commun. Pure Appl. Math., Vol. 59, 1027-1223, 2006.

16. Candes, E., J. Romberg, and T. Tao, "Robust uncertainty principle: Exact signal reconstruction from highly incomplete frequency information," IEEE Trans. Inf. Theory, Vol. 52, 489-509, Feb. 2006.
doi:10.1109/TIT.2005.862083

17. Lustig, M., D. Donoho, and J. Pauly, "Sparse MRI: The application of compressed sensing for rapid MR imaging," Magnetic Reson. Med., Vol. 58, 1182-1195, Apr. 2007.
doi:10.1002/mrm.21391

18. Bian, J., J. Siewedsen, X. Han, et al. "Evaluation of sparse-view reconstruction from flat-panel-detector cone-beam CT," Phys. Med. Biol., Vol. 55, 6575, 2010.
doi:10.1088/0031-9155/55/22/001

19. Han, X., J. Bian, D. Eaker, et al. "Algorithm-enabled low-dose micro-CT imaging," IEEE Trans. Medical Imaging, Vol. 30, 606-620, Mar. 2011.

20. Harmany, Z. T., R. F. Marcia, and R. M. Willett, "Sparsity-regularized photon-limited imaging," IEEE International Symposium on Biomedical Imaging from Nano to Macro, 772-775, 2010.
doi:10.1109/ISBI.2010.5490062

21. Wang, G. and J. Qi, "Direct reconstruction of dynamic PET parameteric images using sparse spectral representation," IEEE International Symposium on Biomedical Imaging: From Nano to Macro, 867-870, 2009.
doi:10.1109/ISBI.2009.5193190

22. Ahthoine, S., J. F. Aujol, Y. Broursier, and C. Melot, "On the efficiency of proximal methods for CBCT and PET reconstruction with sparsity constraint," 4th Workshop on Signal Processing with Adaptive Sparse Structured Representations, 25, 2011.

23. Meinshausen, N. and B. Yu, "LASSO-type recovery of sparse representations for high-dimensional data," Annals of Statistics, Vol. 37, 246-270, 2009.
doi:10.1214/07-AOS582

24. Zhu, C., "Stable recovery of sparse signals via regularized minimization," IEEE Trans. Information Theory, Vol. 54, 3364-3367, Jul. 2008.

25. Mallon, A. and P. Grangeat, "Three-dimensional PET reconstruction with time-of-flight measurement," Phys. Med. Biol., Vol. 37, 717-729, 1992.
doi:10.1088/0031-9155/37/3/016

26. Cho, S., S. Ahn, Q. Li, and R. Leahy, "Analytical properties of time-of-flight PET data," Phys. Medi. Biol., Vol. 53, 2809-2821, 2008.
doi:10.1088/0031-9155/53/11/004

27. Beck, A. and M. Teboulle, "A fast iterative shrinkage-thresholding algorithm for linear inverse problems," SIAM J. Imaging Sciences, Vol. 2, No. 1, 183-202, 2009.
doi:10.1137/080716542

28. Richter, S. and R. De Carlo, "Continuation methods: Theory and applications," IEEE Transactions on Automatic Control, Vol. 28, No. 6, 660-665, 1983.
doi:10.1109/TAC.1983.1103294

29. Wang, Z. and A. C. Bovik, "Image quality assessment: From error visibility to structural similarity," IEEE Trans. Image Processing, Vol. 13, No. 4, 1-14, 2004.
doi:10.1109/TIP.2003.819861

30. Zhdanov, M. and E. Tolstaya, "Minimum support nonlinear parameterization in the solution of a 3D magnetotelluric inverse problem," Inverse Problems, Vol. 20, 937-952, 2004.
doi:10.1088/0266-5611/20/3/017

31. Lois, C., et al. "An assessment of the impact of incorporating time-of-flight information into clinical PET/CT imaging," The Journal of Nuclear Medicine, Vol. 51, No. 2, 237-245, 2010.
doi:10.2967/jnumed.109.068098

32. Daubechies, I., et al. "Iteratively re-weighted least squares minimization for sparse reconvery," Communications of Pure and Applied Mathematics, Vol. 63, No. 1, 1-38, 2010.
doi:10.1002/cpa.20303

33. Vogel, C. R., "Non-convergence of the L-curve regularization parameter selection method," Inverse Problems, Vol. 12, 535-547, 1996.
doi:10.1088/0266-5611/12/4/013

34. Golub, G. H., M. Heath, and G. Wahba, "Generalized cross-validation as a method for choosing a good ridge parameter," Technometrics, Vol. 21, No. 2, 215-223, 1979.
doi:10.1080/00401706.1979.10489751

35. Li, K.-C., "From STEIN's unbiased risk estimates to the method of generalized cross validation," The Annals of Statistics, Vol. 13, No. 4, 1362-1377, 1985.
doi:10.1214/aos/1176349742

Download Full Article (253) View Full Article volume
The EM Academy piers.org jpier.org Who's Who in EM
Copyright © 2022 The Electromagnetics Academy. All Rights Reserved.