V. V. Khryashchev, E. A. Sokolenko, I. V. Apalkov, D. K. Kuykin, Yaroslavl State University, Yaroslavl, Russia

SYNCHROINFO JOURNAL. Volume 5, Number 2 (2019). P. 10-13.


The purpose of this work is to develop efficient and low computational complexity methods for image restoration from phases of their discrete Fourier transform. It is shown how an artificial neural network can be applied to such image restoration problem. Comparisons between neural network approach and iterative method constructed on algorithm of Gerchberg and Saxton are given. In order to reduce computational complexity a complex algorithm, which has combine denominations of different methods is developed. We illustrate the usefulness of this approach by using different images with or without noise. Efficiency and restoration capability of the methods are tested and illustrated through simulation results.

Keywords: restoration, high-quality image, Gerchberg-Saxton algorithm.


[1] H.C. Andrews and B.R. Hunt. Digital Image Restoration. Prentice-Hall, NJ, 1977.
[2] R.C. Gonzalez and R.E. Woods. Digital Image Processing. Prentice-Hall, 2002.
[3] Y.T. Zhou, R. Chellappa and B.K. Jenkiens. Image Restoration Using a Neural Network. IEEE Trans. on Acoustics, Speech and Signal Processing, vol. 36, pp. 1141-1152, 1988.
[4] F. Luo and Z. Bao. Neural Network Approach to Adaptive FIR Filtering and Deconvolution Problems. Proc. IEEE Int. Conf. On Industrial Electronics, Kobe, Japan, pp. 1449-1453, 1991.
[5] H. Stark. Image Recovery: Theory and Applications. Academic Press, New York, NY, 1987.
[6] J.R. Fienup. Space object imaging through the turbulent atmosphere. Opt. Eng., pp. 529-534. 1979.
[7] F-L. Luo and R. Unbehauen. Applied Neural Networks for Signal Processing. Cambridge University Press, 1998.
[8] L. Yin, J. Astola and Y. Neuvo. A New Class of Nonlinear Filters – Neural Filters. IEEE Trans. on Signal Processing, vol. 41, No. 3, pp. 1201-1222, 1999.
[9] D.C. Youla and H. Webb. Image restoration by the method of convex projections: Part I, Theory. IEEE Trans. Medical Imaging, pp. 81-94, 1982.
[10] M.H. Hayes, J.S. Lim and A.V. Oppenheim. Signal reconstruction from phase or magnitude. IEEE Trans. Acoust. Speech Signal Processing, ASSP-28, 672-680, 1980.
[11] R.W. Gerchberg and W.O. Saxton. A practical algorithm for the determination of phase from image and diffraction plane pictures. Optik, 35, 237-246, 1972.
[12] A. Olfat, H. Soltanian-Zadeh. A Neural Network Approach to Magnitude Retrieval. Signal Processing, 81, 1879-1888, 2001.
[13] V.V. Khryashchev E.A. Sokolenko and A.L. Priorov. Neural Network Reconstruction of Amplitude of Discrete Signal from its Phase Spectrum. Proc. of Digital Signal Processing and its Application Conference, Moscow, Russia, pp. 622-625. 2003.