# An analytical iterative statistical algorithm for image reconstruction from projections

International Journal of Applied Mathematics and Computer Science (2014)

- Volume: 24, Issue: 1, page 7-17
- ISSN: 1641-876X

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topRobert Cierniak. "An analytical iterative statistical algorithm for image reconstruction from projections." International Journal of Applied Mathematics and Computer Science 24.1 (2014): 7-17. <http://eudml.org/doc/271929>.

@article{RobertCierniak2014,

abstract = {The main purpose of the paper is to present a statistical model-based iterative approach to the problem of image reconstruction from projections. This originally formulated reconstruction algorithm is based on a maximum likelihood method with an objective adjusted to the probability distribution of measured signals obtained from an x-ray computed tomograph with parallel beam geometry. Various forms of objectives are tested. Experimental results show that an objective that is exactly tailored statistically yields the best results, and that the proposed reconstruction algorithm reconstructs an image with better quality than a conventional algorithm with convolution and back-projection.},

author = {Robert Cierniak},

journal = {International Journal of Applied Mathematics and Computer Science},

keywords = {computed tomography; image reconstruction from projections; statistical reconstruction algorithm},

language = {eng},

number = {1},

pages = {7-17},

title = {An analytical iterative statistical algorithm for image reconstruction from projections},

url = {http://eudml.org/doc/271929},

volume = {24},

year = {2014},

}

TY - JOUR

AU - Robert Cierniak

TI - An analytical iterative statistical algorithm for image reconstruction from projections

JO - International Journal of Applied Mathematics and Computer Science

PY - 2014

VL - 24

IS - 1

SP - 7

EP - 17

AB - The main purpose of the paper is to present a statistical model-based iterative approach to the problem of image reconstruction from projections. This originally formulated reconstruction algorithm is based on a maximum likelihood method with an objective adjusted to the probability distribution of measured signals obtained from an x-ray computed tomograph with parallel beam geometry. Various forms of objectives are tested. Experimental results show that an objective that is exactly tailored statistically yields the best results, and that the proposed reconstruction algorithm reconstructs an image with better quality than a conventional algorithm with convolution and back-projection.

LA - eng

KW - computed tomography; image reconstruction from projections; statistical reconstruction algorithm

UR - http://eudml.org/doc/271929

ER -

## References

top- Bouman, C.A. and Sauer, K.D. (1996). A unified approach to statistical tomography using coordinate descent optimization, IEEE Transactions on Image Processing 5(3): 480-492.
- Bruder, H., Kachelriess, M., Schaller, S., Stierstorfer, K. and Flohr, T. (2000). Single-slice rebinning reconstruction in spiral cone-beam computed tomography, IEEE Transactions on Medical Imaging 9(9): 873-887.
- Cierniak, R. (2006). A novel approach to image reconstruction from projections using Hopfield-type neural network, in L. Rutkowski, R. Tadeusiewicz, L.A. Zadeh and J. Żurada (Eds.), Artificial Intelligence and Soft Computing, Lecture Notes in Artificial Intelligence Vol. 4029, Springer-Verlag, Berlin/Heidelberg, pp. 890-898.
- Cierniak, R. (2008a). A new approach to image reconstruction from projections using a recurrent neural network, Artificial Intelligence in Medicine 43(2): 113-125.
- Cierniak, R. (2008b). A new approach to image reconstruction from projections problem using a recurrent neural network, International Journal of Applied Mathematics and Computer Science 18(2): 147-157, DOI: 10.2478/v10006-008-0014-y.
- Cierniak, R. (2009). New neural network algorithm for image reconstruction from fan-beam projections, Neurocomputing 72(13-15): 3238-3244.
- Cierniak, R. (2010). A three-dimensional neural network based approach to the image reconstruction from projections problem, in L. Rutkowski, R. Scherer, R. Tadeusiewicz, L.A. Zadeh and J. Żurada (Eds.), Artificial Intelligence and Soft Computing, Lecture Notes in Artificial Intelligence, Vol. 6113, Springer-Verlag, Berlin/Heidelberg, pp. 505-514.
- Cierniak, R. (2011). Neural network algorithm for image reconstruction using the grid-friendly projections, Australasian Physical & Engineering Sciences in Medicine 34(3): 375-389.
- DeMan, B. and Basu, S. (2004). Distance-driven projection and backprojection in three dimensions, Physics in Medicine and Biology 49(11): 2463-2475.
- Jain, A.K. (1989). Fundamentals of Digitals Image Processing, Prentice-Hall, Englewood Cliffs, NJ.
- Kachelriess, M., Fuchs, T. and Schaller, S. (2001). Advanced single-slice rebinning for tilted spiral cone-beam CT, Medical Physics 31(6): 1033-1041.
- Kachelriess, M., Knaup, M. and Kalender, W.A. (2004). Extended parallel backprojection for standard three-dimensional and phase-correlated four-dimensional axial and spiral cone-beam CT with arbitrary pitch, arbitrary cone-angle, and 100% dose usage, Medical Physics 31(6): 1623-1641.
- Kachelriess, M., Schaller, S. and Kalender, W.A. (2000). Advanced single-slice rebinning in cone-beam spiral CT, Medical Physics 27(4): 754-773.
- Kaczmarz, S. (1937). Angenaeherte aufloesung von systemen linearer gleichungen, Bulletin International de l'Académie Polonaise des Sciences et des Lettres 35: 355-357.
- Lewitt, R.M. (1983). Reconstruction algorithms: Transform methods, Proceedings of the IEEE 71(3): 390-408.
- Noo, F., Defrise, M. and Clackdoyle, R. (1999). Single-slice rebinning method for helical cone-beam CT, Physics in Medicine and Biology 44(2): 561-570.
- Ren, Q., Dewan, S.K., Li, M., Li, J., Mao, D., Wang, Z. and Hua, Y. (2012). Comparison of adaptive statistical iterative and filtered back projection reconstruction techniques in brain CT, European Journal of Radiology 81(10): 2597-2601.
- Sauer, K. and Bouman, C. (1992). Bayesian estimation of transmission tomograms using segmentation based optimization, IEEE Transactions on Nuclear Science 39(4): 1144-1152.
- Sauer, K.D. and Bouman, C.A. (1993). A local update strategy for iterative reconstruction from projections, IEEE Transactions on Signal Processing 41(3): 480-492. Zbl0825.92085
- Shepp, L.A. and Logan, B.F. (1974). The Fourier reconstruction of a head section, IEEE Transactions on Nuclear Science NS-21: 21-43.
- Silva, A.C., Lawder, H.J., Hara, A., Kujak, J. and Pavlicek, W. (2010). Innovations in CT dose reduction strategy: Application of the adaptive statistical iterative reconstruction algorithm, American Journal of Roentgenology 194(1): 191-199.
- Thibault, J.B., Sauer, K.D., Bouman, C.A. and Hsieh, J. (2007). A three-dimensional statistical approach to improved image quality for multislice helical CT, Medical Physics 34(11): 4526-4544.
- Xu, J. and Tsui, B.M.W. (2009). Electronic noise modeling in statistical iterative reconstruction, IEEE Transactions on Image Processing 18(6): 1228-1238.
- Yanagawa, M., Honda, O., Yoshida, S., Kikuyama, A., Inoue, A., Sumikawa, H., Koyama, M. and Tomiyama, N. (2010). Adaptive statistical iterative reconstruction technique for pulmonary CT: Image quality of the cadeveric lung on standard- and reduced-dose CT, Academic Radiology 17(10): 1259-1266.
- Zhou, Y., Thibault, J.B., Bouman, C.A., Sauer, K.D. and Hsieh, J. (2011). Fast model-based x-ray CT reconstruction using spatially non-homogeneous ICD optimization, IEEE Transactions on Image Processing 20(1): 161-175.

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