Supplementary Files
Keywords
compressive sensing
x-rays
coded aperture
transmittance
How to Cite
Abstract
Computed tomography (CT) allows the three-dimensional internal structure reconstruction of an object illuminated with X-ray light. In CT, a set of two-dimensional projections are taken to reconstruct the underlying object structure. The number of projections needed for sensing a CT scene is determined by the Nyquist limit. In some cases, the imposed projections number is excessive. Compressive sensing (CS) has emerged as a new sampling technique requiring fewer projections than those specified by the Nyquist criterion. Instead of measuring the simples directly, they are encoded before being integrated into the detector. This paper describes a CS system for CT based on coded apertures. An optimized value of transmittance and an aperture distribution are selected such that the quality of reconstruction is maximized. Simulations show that results in reconstruction with 50% of measurements are comparable with the traditional CT method based on Nyquist criterion. Similarly, results indicate that the PSNR of reconstructed images can be controlled according to the number of projections taken.
[2] S. Chen, H. Chen, S. Li, J. Li, and S. Li, “Evaluation measurement of accuracy of industrial computed tomography,” Nondestructive Evaluation/Testing: New Technology & Application (FENDT), 2013 Far East Forum on, Jinan, pp. 177-180, 2013.
[3] V. Cnudde and M.N. Boone, “High-resolution X-ray computed tomography in geosciences: A review of the current technology and applications,” Earth-Sci. Rev., vol. 123, pp. 1-17, 2013.
[4] J. Dewanckele, T. De Kock, G. Fronteau, H. Derluyn, P. Vontobel, M. Dierick, L. Van Hoorebeke, P. Jacobs, V. Cnudde, “Neutron radiography and X-ray computed tomography for quantifying weathering and water uptake processes inside porous limestone used as building material,” Mater. Charact., vol. 88, pp. 86-99, 2014.
[5] Shannon, C. E., “Communication in the presence of noise,” in Proc. of the IEEE, vol. 86, no. 2, pp. 447–457, 1998.
[6] R. Smith-Bindman, J. Lipson, R. Marcus, K.-P. Kim, M. Mahesh, R. Gould, A. Berrington de González, and D. L. Miglioretti, “Radiation dose associated with common computed tomography examinations and the associated lifetime attributable risk of cancer,” Arch. Intern. Med., vol. 169, pp. 2078–86, 2009.
[7] A. Wagadarikar, R. John, R. Willett, and D. Brady, “Single disperser design for coded aperture snapshot spectral imaging,” Appl. Opt., vol. 47, pp. B44–51, 2008.
[8] D. L. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory, vol. 52, pp. 1289–1306, 2006.
[9] E. Maire and P.J. Withers, “Quantitative X-ray tomography,” Int. Mater. Rev., vol. 59, pp. 1–43, Jan. 2014.
[10] K. Choi and D. J. Brady, “Coded aperture computed tomography,” in Proc. SPIE 7468, vol. 7468, p. 74680B–74680B–10, 2009.
[11] M.M. Sevak, F.N. Thakkar, R.K. Kher, C.K. Modi, “CT image compression using compressive sensing and wavelet transform,” Int. Conf. on Communication Systems and Network Technologies, pp. 138–142, 2012.
[12] G. Wang, H. Yu, and B. De Man, “An outlook on x-ray CT research and development.” Med. Phys., vol. 35, pp. 1051-1064, 2008.
[13] E. Niemi, M. Lassas, A. Kallonen, L. Harhanen, K. Hämäläinen, and S. Siltanen, “Dynamic multi-source X-ray tomography using a spacetime level set method,” J. Comput. Phys., vol. 291, pp. 218-237, 2015.
[14] E. Niemi, M. Lassas, and S. Siltanen, S., “Dynamic X-ray tomography with multiple sources,” in Image and Signal Processing and Analysis (ISPA), 2013 8th International Symposium on, pp. 618-621, 2013.
[15] O. Espitia, Y. Mejía, and H. Arguello, “Tomografía computarizada: proceso de adquisición, tecnología y estado actual,” Tecnura, vol. 20, no. 47, pp. 119-135, 2016.
[16] S. Qaisar, R.M. Bilal, W. Iqbal, M. Maureen, and S. Lee, “Compressive sensing: From theory to applications, a survey,” Commun. Networks, vol. 15, pp. 443–456, 2013.
[17] M. B. Wakin, “An introduction to compressive sampling,” IEEE Signal Process. Mag., vol. 25, no. 2. pp. 21–30, 2008.
[18] E. J. Candes, J. Romberg, and T. Tao, “Robust uncertainty principles: Exact signal frequency information,” IEEE Trans. Inf. Theory, vol. 52, pp. 489–509, 2006.
[19] E. J. Candes and T. Tao, “Near-optimal signal recovery from random projections: Universal encoding strategies,” IEEE Trans. Inf. Theory, vol. 52, pp. 5406–5425, 2006.
[20] G.R. Arce, D.J. Carin, H. Argüello, and D.S. Kittle, “Compressive coded aperture spectral imaging: An introduction,” IEEE Signal Process. Mag., vol. 31, no. 1, pp. 105–115, 2013.
[21] K. P. MacCabe, A.D. Holmgren, M.P. Tornai, and D.J. Brady, “Snapshot 2D tomography via coded aperture X-ray scatter imaging.,” Appl. Opt., vol. 52, no. 19, 2013.
[22] D.F. Galvis, Y.H. Mejía, and H. Argüello, “Efficient reconstruction of Raman spectroscopy imaging based on compressive sensing,” DYNA, vol. 81, no. 188, pp. 116–124, 2014.
[23] F. Xu, W. Xu, M. Jones, B. Keszthelyi, J. Sedat, D. Agard, and K. Mueller, “On the efficiency of iterative ordered subset reconstruction algorithms for acceleration on GPUs.,” Comput. Method Prog. Biomed, vol. 98, no. 3, pp. 261–270, 2010.
[24] Má. A. T. Figueiredo, R. D. Nowak, and S. J. Wright, “Gradient projection for sparse reconstruction: Application to compressed sensing and other inverse problems,” IEEE J. Sel. Top. Signal Process., vol. 1, no. 4, pp. 586–597, Dec. 2007.
[25] J.M. Bioucas-Dias and M. a T. Figueiredo, “A new twIst: two-step iterative shrinkage/thresholding algorithms for image restoration,” IEEE Trans. Image Process., vol. 16, no. 12, pp. 2992–3004.
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