A New Approach to Image Reconstruction from Projections Using a Recurrent Neural Network

Averbuch A., Coifman R.R., Donoho D.L., Israeli M. and Waldén J. (2001). A notion of Radon transform for data in a Cartesian grid, which is rapidly computable, algebraically exact, geometrically faithful and invertible, Technical report TR No. 2001-11, Department of Statistics, Stanford University, USA.Search in Google Scholar

Censor Y. (1983). Finite series-expansion reconstruction methods, Proceeding of the IEEE 71(3): 409-419.10.1109/PROC.1983.12598Search in Google Scholar

Cichocki A., Unbehauen R., Lendl M. and Weinzierl K. (1995). Neural networks for linear inverse problems with incomplete data especially in application to signal and image reconstruction, Neurocomputing 8: 7-41.10.1016/0925-2312(94)E0063-WSearch in Google Scholar

Cierniak R. and Rutkowski L. (2000). On image compression by competitive neural networks and optimal linear predictors, Signal Processing: Image Communication 15(6): 559-565.10.1016/S0923-5965(99)00013-2Search in Google Scholar

Cierniak R. (2002). Image reconstruction from projection using unsupervised neural network, Proceedings of the Joint 1-st International Conference on Soft Computing and Intelligent Systems and 3-rd International Symposium on Advanced Intelligent Systems, Tsukuba, Japan.Search in Google Scholar

Cierniak R. (2006). A novel approach to image reconstruction from projections using Hopfield-type neural network, in Rutkowski L., Tadeusiewicz R., Zadeh L. A., Żurada J. (Eds.), Proceedings of the 8-th International Conference on Artificial Intelligence and Soft Computing, Zakopane, Poland, LNAI, Springer, Berlin, pp. 890-898.Search in Google Scholar

Cormack A.M. (1963). Representation of a function by its line integrals with some radiological application, Journal of Applied Physics 34: 2722-2727.10.1063/1.1729798Search in Google Scholar

Gordon R., Bender R. and Herman G.T. (1970). Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography, Journal of Theoretical Biology 29: 471-481.10.1016/0022-5193(70)90109-8Search in Google Scholar

Hopfield J.J. (1982). Neural networks and physical systems with emergent collective computational abilities, Proceedings of the National Academy of Sciences of the USA 79: 2554-2558.10.1073/pnas.79.8.2554Search in Google Scholar

Ingman D. and Merlis Y. (1992). Maximum entropy signal reconstruction with neural networks, IEEE Transactions on Neural Networks 3: 195-201.10.1109/72.125860Search in Google Scholar

Jaene B. (1991). Digital Image Processing - Concepts, Algoritms and Scientific Applications, Springer, Berlin, Heidelberg.Search in Google Scholar

Jain A.K. (1989). Fundamentals of Digital Image Processing, Prentice Hall, Englewood Cliffs, NJ.Search in Google Scholar

Kaczmarz S. (1937). Angeneaherte Aufloesung von Systemen Linearer Gleichungen, Bulletin de l'Académie Polonaise des Sciences et Lettres 35: 355-357.Search in Google Scholar

Kak A.C. and Slanley M. (1988). Principles of Computerized Tomographic Imaging, IEEE Press, New York.Search in Google Scholar

Kerr J.P. and Barlett E.B. (1995a). A statistically tailored neural network approach to tomographic image reconstruction, Medical Physics 22: 601-610.10.1118/1.597586Search in Google Scholar

Kerr J.P. and Barlett E.B. (1995b). Medical image processing utilizing neural networks trained on a massively parallel computer, Computers in Biology and Medicine 25: 393-403.10.1016/0010-4825(95)00017-XSearch in Google Scholar

Kerr J.P. and Barlett E.B. (1995c). Neural network reconstruction of single-photon emission computed tomography images, Journal of Digital Imaging 8: 116-126.10.1007/BF031680857488654Search in Google Scholar

Kingston A. and Svalbe I. (2003). Mapping between digital and continuous projections via the discrete Radon transform in Fourier space, Proceedings of the 7-th Conference on Digital Image Computing: Techniques and Applications, Sydney, pp. 263-272.Search in Google Scholar

Knoll P., Mirzaei S., Muller A., Leitha T., Koriska K., Kohn H. and Neumann M. (1999). An artificial neural net and error backpropagation to reconstruct single photon emission computerized tomography data, Medical Physics 26: 244-248.10.1118/1.598511Search in Google Scholar

Lewitt R.M. (1983). Reconstruction algorithms: Transform methods, Proceeding of the IEEE 71(3): 390-408.10.1109/PROC.1983.12597Search in Google Scholar

Luo F.-L. and Unbehauen R. (1998). Applied Neural Networks for Signal Processing, Cambridge University Press, Cambridge, UK.Search in Google Scholar

Munllay M.T., Floyd C.E., Bowsher J.E. and Coleman R. E. (1994). An artificial neural network approach to quantitative single photon emission computed tomographic reconstruction with collimator, attenuation and scatter compensation, Medical Physics 21: 1889-1899.10.1118/1.597167Search in Google Scholar

Ramachandran G.N. and Lakshminarayanan A.V. (1971). Three-dimensional reconstruction from radiographs and electron micrographs: II. Application of convolutions instead of Fourier transforms, Proceedings of the National Academy of Sciences of the USA 68: 2236-2240.Search in Google Scholar

Srinivasan V., Han Y.K. and Ong S.H. (1993). Image reconstruction by a Hopfield neural network, Image and Vision Computing 11(5): 278-282.10.1016/0262-8856(93)90005-2Search in Google Scholar

Wang Y. and Wahl F.M. (1997). Vector-entropy optimization-based neural-network approach to image reconstruction from projections, IEEE Transaction on Neural Networks 8(5): 1008-1014.10.1109/72.62320218255703Search in Google Scholar