Search search
submit Submit
Publication Date
to
Vol. 158
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
2017-01-25
Image Reconstruction from Highly Sparse and Limited Angular Diffraction Tomography Using Compressed Sensing Approach
By
Pavel Roy Paladhi,

    Dr. Pavel Roy Paladhi

    Department of Electrical and Computer Engineering

    Michigan State University

    USA

    Homepage

Amin Tayebi,

    Dr. Amin Tayebi

    Department of Electrical and Computer Engineering

    Michigan State University

    USA

    Homepage

Portia Banerjee,

    Dr. Portia Banerjee

    Department of Electrical and Computer Engineering

    Michigan State University

    USA

    Homepage

Lalita Udpa,

    Dr. Lalita Udpa

    Michigan State University

    USA

    Homepage

Satish Udpa

    Dr. Satish Udpa

    Department of Electrical and Computer Engineering

    Michigan State University

    USA

    Homepage

Progress In Electromagnetics Research, Vol. 158, 21-36, 2017
doi:10.2528/PIER16111501
Abstract
Diffraction tomography (DT) from limited projection data has been an active research topic for over three decades. The interest has been steadily fueled due to its application in multiple disciplines including medical imaging, structural health monitoring and non-destructive evaluation to name a few. This paper explores the applicability of compressed sensing to recover complex-valued objective functions (e.g., complex permittivity in microwave tomography). Generally, compressed sensing based tomographic reconstruction has been studied under full angular access. In this paper, the effect of lowering the angular access in addition to highly limited number of projection data is explored. The effectiveness of the reconstruction methods is tested with severely limited dataset which would render reconstruction impossible by traditional iterative approximation methods. Furthermore, results show that complex-valued phantoms can be reconstructed from as few as 15 projections from 120˚ coverage, a significant finding. In this study, the Total Variation (TV) has been used as the l1 norm within the compressed sensing framework. The robustness of the algorithm in presence of noise is discussed. Use of multiple sparse domains has also been explored briefly. The results show the effectiveness of TV as a regularization parameter even for complex-valued images under the compressed sensing regime. This is a pertinent observation as TV is a simple norm to implement. For a large class of images, especially in medical imaging, this implies the availability of a steady l1 norm for easy implementation of compressed sensing reconstruction for complex-valued images.
Citation
Pavel Roy Paladhi, Amin Tayebi, Portia Banerjee, Lalita Udpa, and Satish Udpa, "Image Reconstruction from Highly Sparse and Limited Angular Diffraction Tomography Using Compressed Sensing Approach," Progress In Electromagnetics Research, Vol. 158, 21-36, 2017.
doi:10.2528/PIER16111501
References

1. Kak, A. C. and M. Slaney, "Principles of computerized tomographic imaging," Society for Industrial and Applied Mathematics, 2001.

2. Paladhi, P., A. Sinha, A. Tayebi, L. Udpa, and A. Tamburrino, "Data redundancy in diffraction tomography," 2015 31st International Review of Progress in Applied Computational Electromagnetics (ACES), 1-2, March 2015.

3. Paladhi, P. R., A. Tayebi, L. Udpa, S. Udpa, and A. Sinha, "Class of backpropagation techniques for limited-angle reconstruction in microwave tomography," AIP Conference Proceedings, Vol. 1650, No. 1, 509-518, 2015.
doi:10.1063/1.4914648

4. Paladhi, P. R., A. Sinha, A. Tayebi, L. Udpa, and S. S. Udpa, "Improved backpropagation algorithms by exploiting data redundancy in limited-angle diffraction tomography," Progress In Electromagnetics Research B, Vol. 66, 1-13, 2016.
doi:10.2528/PIERB15120204

5. Paladhi, P. R., J. Klaser, A. Tayebi, L. Udpa, and S. Udpa, "Reconstruction algorithm for limited-angle diffraction tomography for microwave NDE," AIP Conference Proceedings, Vol. 1581, No. 1, 1544-1551, 2014.
doi:10.1063/1.4865007

6. LaRoque, S. J., E. Y. Sidky, and X. Pan, "Accurate image reconstruction from few-view and limited-angle data in diffraction tomography," JOSA A, Vol. 25, No. 7, 1772-1782, 2008.
doi:10.1364/JOSAA.25.001772

7. Sung, Y. and R. R. Dasari, "Deterministic regularization of three-dimensional optical diffraction tomography," JOSA A, Vol. 28, No. 8, 1554-1561, 2011.
doi:10.1364/JOSAA.28.001554

8. Donoho, D. L., "Compressed sensing," IEEE Transactions on Information Theory, Vol. 52, No. 4, 1289-1306, 2006.
doi:10.1109/TIT.2006.871582

9. Candes, E. J. and M. B. Wakin, "An introduction to compressive sampling," IEEE Signal Processing Magazine, Vol. 25, No. 2, 21-30, 2008.
doi:10.1109/MSP.2007.914731

10. Candes, E. J., J. K. Romberg, and T. Tao, "Stable signal recovery from incomplete and inaccurate measurements," Communications on Pure and Applied Mathematics, Vol. 59, No. 8, 1207-1223, 2006.
doi:10.1002/cpa.20124

11. Candes, E. J., J. Romberg, and T. Tao, "Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information," IEEE Transactions on Information Theory, Vol. 52, No. 2, 489-509, 2006.
doi:10.1109/TIT.2005.862083

12. Lustig, M., D. Donoho, and J. M. Pauly, "Sparse MRI: The application of compressed sensing for rapid MR imaging," Magnetic Resonance in Medicine, Vol. 58, No. 6, 1182-1195, 2007.
doi:10.1002/mrm.21391

13. Lustig, M., D. Donoho, J. Santos, and J. Pauly, "Compressed sensing MRI," IEEE Signal Processing Magazine, Vol. 25, No. 2, 72-82, March 2008.
doi:10.1109/MSP.2007.914728

14. Chartrand, R., "Fast algorithms for nonconvex compressive sensing: MRI reconstruction from very few data," IEEE International Symposium on Biomedical Imaging: From Nano to Macro, 2009, ISBI'09, 262-265, 2009.
doi:10.1109/ISBI.2009.5193034

15. Gamper, U., P. Boesiger, and S. Kozerke, "Compressed sensing in dynamic MRI," Magnetic Resonance in Medicine, Vol. 59, No. 2, 365-373, 2008.
doi:10.1002/mrm.21477

16. Hua, S., M. Ding, and M. Yuchi, "Sparse-view ultrasound diffraction tomography using compressed sensing with nonuniform fit," Computational and Mathematical Methods in Medicine, Vol. 2014, 2014.

17. Zhu, Z., K. Wahid, P. Babyn, D. Cooper, I. Pratt, and Y. Carter, "Improved compressed sensing- based algorithm for sparse-view CT image reconstruction," Computational and Mathematical Methods in Medicine, Vol. 2013, 2013.

18. Mishali, M. and Y. C. Eldar, "From theory to practice: Sub-nyquist sampling of sparse wideband analog signals," IEEE Journal of Selected Topics in Signal Processing, Vol. 4, No. 2, 375-391, 2010.
doi:10.1109/JSTSP.2010.2042414

19. Liu, J., C. Z. Han, X. H. Yao, and F. Lian, "A novel compressed sensing based method for space time signal processing for airborne radars," Progress In Electromagnetics Research B, Vol. 52, 139-163, 2013.
doi:10.2528/PIERB13033105

20. Baraniuk, R. and P. Steeghs, "Compressive radar imaging," 2007 IEEE Radar Conference, 128-133, 2007.
doi:10.1109/RADAR.2007.374203

21. Yang, M. and G. Zhang, "Parameter identifiability of monostatic mimo chaotic radar using compressed sensing," Progress In Electromagnetics Research B, Vol. 44, 367-382, 2012.
doi:10.2528/PIERB12072712

22. El-Khamy, M., M. Farrag, and M. El-Sharkawy, "Wide-band secure compressed spectrum sensing for cognitive radio systems," Progress In Electromagnetics Research B, Vol. 53, 47-71, 2013.
doi:10.2528/PIERB13051805

23. Zhang, Y., L. Wu, B. Peterson, and Z. Dong, "A two-level iterative reconstruction method for compressed sensing MRI," Journal of Electromagnetic Waves and Applications, Vol. 25, No. 8-9, 1081-1091, 2011.
doi:10.1163/156939311795762024

24. Zhang, Y., S. Wang, G. Ji, and Z. Dong, "Exponential wavelet iterative shrinkage thresholding algorithm with random shift for compressed sensing magnetic resonance imaging," IEEJ Transactions on Electrical and Electronic Engineering, Vol. 10, No. 1, 116-117, 2015.
doi:10.1002/tee.22059

25. Zhang, Y., B. S. Peterson, G. Ji, and Z. Dong, "Energy preserved sampling for compressed sensing MRI," Computational and Mathematical Methods in Medicine, Vol. 2014, 2014.

26. Devaney, A., "A filtered backpropagation algorithm for diffraction tomography," Ultrasonic Imaging, Vol. 4, No. 4, 336-350, 1982.
doi:10.1177/016173468200400404

27. Sung, Y., W. Choi, C. Fang-Yen, K. Badizadegan, R. R. Dasari, and M. S. Feld, "Optical diffraction tomography for high resolution live cell imaging," Optics Express, Vol. 17, No. 1, 266-277, 2009.
doi:10.1364/OE.17.000266

28. Catapano, I., L. Di Donato, L. Crocco, O. M. Bucci, A. F. Morabito, T. Isernia, and R. Massa, "On quantitative microwave tomography of female breast," Progress In Electromagnetics Research, Vol. 97, 75-93, 2009.
doi:10.2528/PIER09080604

29. Drogoudis, D. G., G. A. Kyriacou, and J. N. Sahalos, "Microwave tomography employing an adjoint network based sensitivity matrix," Progress In Electromagnetics Research, Vol. 94, 213-242, 2009.
doi:10.2528/PIER09060808

30. Baran, A., D. J. Kurrant, A. Zakaria, E. C. Fear, and J. LoVetri, "Breast imaging using microwave tomography with radar-based tissue-regions estimation," Progress In Electromagnetics Research, Vol. 149, 161-171, 2014.
doi:10.2528/PIER14080606

31. Tayebi, A., J. Tang, P. R. Paladhi, L. Udpa, and S. Udpa, "Design and development of an electrically-controlled beam steering mirror for microwave tomography," AIP Conference Proceedings, Vol. 1650, 501-508, AIP Publishing, 2015.

32. Tayebi, A., J. Tang, P. R. Paladhi, L. Udpa, S. S. Udpa, and E. J. Rothwell, "Dynamic beam shaping using a dual-band electronically tunable reflectarray antenna," IEEE Transactions on Antennas and Propagation, Vol. 63, No. 10, 4534-4539, 2015.
doi:10.1109/TAP.2015.2456939

33. Tayebi, A., P. Roy Paladhi, L. Udpa, and S. Udpa, "A novel time reversal based microwave imaging system," Progress In Electromagnetics Research C, Vol. 62, 139-147, 2016.
doi:10.2528/PIERC16012403

34. Candes, E. J. and T. Tao, "Decoding by linear programming," IEEE Transactions on Information Theory, Vol. 51, No. 12, 4203-4215, 2005.
doi:10.1109/TIT.2005.858979

35. Candes, E. and J. Romberg, "Sparsity and incoherence in compressive sampling," Inverse Problems, Vol. 23, No. 3, 969, 2007.
doi:10.1088/0266-5611/23/3/008

36. Boyd, S. and L. Vandenberghe, Convex Optimization, Cambridge University Press, 2004.
doi:10.1017/CBO9780511804441

37. Bronstein, M. M., A. M. Bronstein, M. Zibulevsky, and H. Azhari, "Reconstruction in diffraction ultrasound tomography using nonuniform fit," IEEE Transactions on Medical Imaging, Vol. 21, No. 11, 1395-1401, 2002.
doi:10.1109/TMI.2002.806423

38. Liberti, L. and N. Maculan, "Global optimization: From theory to implementation," Springer Science & Business Media, Vol. 84, 2006.

39. Sturm, J. F., "Using sedumi 1.02, a matlab toolbox for optimization over symmetric cones," Optimization Methods and Software, Vol. 11, No. 1--4, 625-653, 1999.
doi:10.1080/10556789908805766

Download Full Article (390) View Full Article volume
The EM Academy piers.org jpier.org Who's Who in EM
Copyright © 2022 The Electromagnetics Academy. All Rights Reserved.