Zhurnal Radioelektroniki - Journal of Radio Electronics. eISSN 1684-1719. 2022. №9
pdf) in Russian (
ALGORITHMS OF THE METHOD OF AMPLITUDE ITERATIONS
AND POCS FOR THE RECONSTRUCTION
OF SPARSE TWO-DIMENSIONAL SIGNALS
Kotelnikov IRE RAS, Fryazino branch
141120, Russia, Fryazino, Vvedenskogo sq., 1
The paper was received August 31, 2022.
Abstract. The paper presents algorithms of the method of amplitude iterations (MAI) and the method of projections onto convex sets (POCS) adapted for the reconstruction of sparse two-dimensional signals. Digital images with significantly different autocorrelation functions (ACF) are selected as examples for the practical application of MAI and POCS. The calculations carried out allow us to conclude that it is possible in principle to use MAI and POCS to restore sparse images both for the reconstruction of lacunae and in order to reduce the amount of data.
Key words: remote sensing, sparse digital images, image processing, method of amplitude iterations, method of projections onto convex sets.
Financing: The work was carried out within the framework of the state task of the Kotelnikov Institute of Radioengineering and Electronics (IRE) of Russian Academy of Sciences № 075-01133-22-00.
Corresponding author: Kokoshkin Alexander Vladimirovich, firstname.lastname@example.org
1. Yeh S., Stark H. Iterative and one-step reconstruction from nonuniform samples by convex projections. Journal of the Optical Society of America. 1990. V.7. №3. P.491-499. https://doi.org/10.1364/JOSAA.7.000491
2. Stasiński R., Konrad J. Improved POCS-based image reconstruction from irregularly-spaced samples. Proceedings of the IEEE International Conference on Image Processing (ICIP '00). 2002. P.1-4.
3. Park J., Park D-C, Marks R.J. II, El-Sharkawi M.A. Block loss recovery in DCT image encoding using POCS. Proceedings of the IEEE International Symposium on Circuits and Systems. 2002. https://doi.org/10.1109/ISCAS.2002.1010686
4. Huang H., Makur A. A new iterative reconstruction scheme for signal reconstruction. Proceedings of the IEEE Asia Pacific Conference on Circuits and Systems (APCCAS '08). 2008. https://doi.org/10.1109/APCCAS.2008.4746028
5. Ogawa T., Haseyama M. Adaptive reconstruction method of missing texture based on projection onto convex sets. Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP '07). 2007. https://doi.org/10.1109/ICASSP.2007.366003
6. Chen J., Zhang L., Luo J., Zhu Y. MRI reconstruction from 2D partial k-space using POCS algorithm. Proceedings of the 3rd International Conference on Bioinformatics and Biomedical Engineering (ICBBE '09). 2009. https://doi.org/10.1109/ICBBE.2009.5163089
7. Feichtinger H.G., Kozek W., Strohmer T. Reconstruction of signals from irregular samples of its short-time Fourier transform. Wavelet Applications in Signal and Image Processing III. 1995. V.2569. P.140-150. https://doi.org/10.1117/12.217570
8. Guven H.E., Ozaktas H.M., Cetin A.E., Barshan B. Signal recovery from partial fractional Fourier domain information and its applications. IET Signal Processing. 2008. V.2. №1. P.15-25. http://doi.org/10.1049/iet-spr:20070017
9. Serbes A., Durak L. Optimum signal and image recovery by the method of alternating projections in fractional Fourier domains. Communications in Nonlinear Science and Numerical Simulation. 2010. V.15. №3. P.675-689.
10. Kokoshkin A.V., Korotkov V.A., Novichikhin E.P. Reconstruction of Acoustic Signals According to Incomplete Data. Journal of Communications Technology and Electronics. 2020. V.65. №12. P.1399-1406. https://doi.org/10.31857/S0033849420120104
11. Kokoshkin A.V., Novichikhin E.P. Application of the Interpolation Method of Sequential Computation of the Fourier Spectrum to Sparse Images. REHNSIT: Radioehlektronika. Nanosistemy. Informatsionnye tekhnologii [RENSIT: Radioelectronics. Nanosystems. Information Technologies]. 2022. V.14. №2. P.165-174. https://doi.org/10.17725/rensit.2022.14.165 (In Russian)
12. Bregman L.M. Finding the common point of convex sets by the method of successive projections. Doklady Akademii Nauk SSSR [Documents of the Academy of Sciences of the USSR]. 1965 V.162. №3. P.487-490. (In Russian)
13. Gubin L.G., Polyak B.T., Raik E.V. The method of projections for finding the common point of convex sets. USSR Computational Mathematics and Mathematical Physics. 1967. V.7. №6. P.1-24. https://doi.org/10.1016/0041-5553(67)90113-9
14. Oh J., Senay S., Chaparro L. Signal Reconstruction from Nonuniformly Spaced Samples Using Evolutionary Slepian Transform-Based POCS. Hindawi Publishing Corporation, EURASIP Journal on Advances in Signal Processing. V.2010. https://doi.org/10.1155/2010/367317
Kokoshkin A.V. Algorithms of the method of amplitude iterations and POCS for the reconstruction of sparse two-dimensional signals. Zhurnal radioehlektroniki [Journal of Radio Electronics] [online]. 2022. №9. https://doi.org/10.30898/1684-1719.2022.9.7 (In Russian)