Algorithms for Digital Processing of Measurement Data Providing Angular Superresolution

Incorrect one- and two-dimensional inverse problems of reconstructing images of objects with angular resolutionexceeding the Rayleigh criterion are considered. The technique is based on the solution of inverse problems of source reconstruction signals described Fredholm integral equations. Algebraic methods and algorithms for processing dataobtained by measuring systems in order to achieve angular superresolution are presented. Angular superresolution allows you to detail images of objects, solve problems of their recognition and identification on this basis. The efficiency of using algorithms based on developed algebraic methods and their modifications in parameterization the inverse problems under study and further reconstructing approximate images of objects of various types is shown. It is shown that the noise immunity of the obtained solutions exceeds many known approaches. The results of numerical experiments demonstrate the possibility of obtaining images with a resolution exceeding the Rayleigh criterion by 2-6 times at small values of the signal-to-noise ratio. The ways of further increasing the degree of superresolution based on the intelligent analysis of measurement data are described. On the basis of the preliminary information on a source of signals algorithms allow to increase consistently the effective angular resolution before achievement greatest possible for a solved problem. Algorithms of secondary processing of the information necessary for it are described. It is found that the proposed symmetrization algorithm improves the quality of solutions to the inverse problems under consideration and their stability. The examples demonstrate the successful application of modified algebraic methods and algorithms for obtaining images of the objects under study in the presence of a priori information about the solution. The results of numerical studies show that the presented methods of digital processing of received signals allow us to restore the angular coordinates of individual objects under study and their elements with super-resolution with good accuracy. The adequacy and stability of the solutions were verified by conducting numerical experiments on a mathematical model. It was shown that the stability of solutions, especially at a significant level of random components, is higher than that of many other methods. The limiting possibilities of increasing the effective angular resolution and the accuracy of image reconstruction of signal sources, depending on the level of random components in the data utilized, are found. The effective angular resolution achieved in this case is 2—10 times higher than the Rayleigh criterion. The minimum required signal-to-noise ratio for obtaining adequate solutions with super-resolution is 13—16 dB for the described methods, which is significantly less than for the known methods. The relative simplicity of the presented methods allows you to use inexpensive computing devices and work in real time.

1. Kasturiwala S. B., Ladhake S. A. Superresolution: A novel application to image restoration, International Journal on Computer Science and Engineering, 2010, no. 5, pp. 1659—1664.

2. Uttam S., Goodman N. A. Superresolution of coherent sources in real-beam Data, IEEE Trans. on Aerospace and Electronic Systems, 2010, vol. 46, no. 3, pp. 1557—1566.

3. Park S. C., Park M. K., Kang M. G. Super-resolution image reconstruction: a technical overview, IEEE Signal Processing Magazine, 2003, vol. 20(3), pp. 21—36.

4. Du ng G. V. , Ku likov N. V. Analysis of noise immunity of reception of signals with multiple phase shift keying under the influence of scanning interference, Russian technological journal, 2018, vol.6, no. 6, pp. 5—12.

5. Waweru N. P., Konditi D. B. O., Langat P. K. Performance Analysis of MUSIC Root-MUSIC and ESPRIT, DOA Estimation Algorithm. International Journal of Electrical Computer Energetic Electronic and Comm. Engineering, 2014, vol. 8, no. 1, pp. 209—216.

6. Rao B. D., Hari K. V. S. Performance analysis of RootMusic, IEEE Trans. on Acoustics, Speech, and Signal Processing,1989, v. 37, no. 12, pp. 1939— 1949.

7. Kim K. T., Seo D. K, Kim H. T. Ecient radar target recognition using the MUSIC algorithm and invariant features, IEEE Trans. Antennas and Propagation, 2002, vol. 50, no. 3, pp. 325—337.

8. Lavate T. B., Kokate V. K., Sapkal A. M. Performance Analysis of MUSIC and ESPRIT, DOA Estimation Algorithms for Adaptive Array Smart Antenna in Mobile Communication.2nd Int. Conf. on Computer and Network Technology ICCNT, United States,2010, pp. 308—311.

9. Sroubek F., Cristobal G., Flusser J. Simultaneous SuperResolution and Blind Deconvolution, Journal of Physics: Conference Series, 2008, 124(1): 012048.10. Almeida M. S., Figueiredo M. A. Deconvolving images with unknown boundaries using the alternating direction method of multipliers, IEEE Trans. Image Process, 2013, vol. 22, no. 8, pp. 3074—3086.

10. Dudík M., Phillips S. J., Schapire R. E. Maximum entropy density estimation with generalized regularization and an application to species distribution modeling, Journal of Machine Learning Research, 2007, no. 8, pp. 1217—1260.

11. Borgiotti G. V., Kaplan L. J. Superresolution of uncorrected interference sources by using adaptive array technique, IEEE Trans. Antennas Propagat.,1979, vol. AP-27, pp. 842—845.

12. Tan W. Q., Hou Y. G. Estimation of direction of source arrival based upon MUSIC and Capon, Journal of Nanchang Institute of Technology, 2008, no. 27(1), pp.20—23.

13. Stoica P., Sharman K. C. Maximum likelihood methods for direction-of-arrival estimation, IEEE Trans. on Acoustics, Speech and Signal Processing, 1990, no. 38(7), pp. 1132—1143.

14. Cetin M., Karl W. C. Feature-enhanced synthetic aperture radar image formation based on nonquadratic regularization, IEEE Trans. Image Processing, 2001, vol. 10, no. 4, pp. 623—631.

15. Lagovsky B. A., Samokhin A. B., Shestopalov Y. V. Increasing effective angular resolution measuring systems based on antenna arrays, Proc. 2016 URSI Int. Symp. Electromagnetic Theory (EMTS), Espoo, Finland, pp. 432—434, 2016.

16. Lagovsky B. A., Chikina A. G. Superresolution in signal processing using a priori information. IEEE, Progress in Electromagnetics Research Symp., St. Petersburg,2017, pp. 944—947.

17. Lagovsky B. A., Samokhin A. B., Shestopalov Y. V. Increasing the effective angular resolution measuring systems based on antenna arrays, Proc. of the 2016 URSI International Symposium on Electromagnetic Theory (EMTS), Espoo, Finland, 2016, pp. 434—436.

18. Morse P., Feshbach H. Methods of Theoretical Physics, McGraw-Hill, Science/Engineering/Math., 1953, 1978 p.

19. Lagovsky B. A., Samokhin A. B. Image Restoration of Two-dimensional Signal Sources with Superresolution, Progress In Electromagnetics Research Symposium Proceedings (PIERS), Stockholm, 2013, pp. 315—319.

20. Lagovsky B. A., Samokhin A. B., Shestopalov Y. V. Creating Two-Dimensional Images of Objects with High Angular Resolution, 2018 IEEE Asia-Pacific Conference on Antennas and Propagation (APCAP), 2018, pp. 114—115.

21. Lagovsky B. A., Samokhin A. B., Tripathy M. Superresolution in problems of remote sensing, ITM Web of Conferences. 29 th International Crimean Conference Microwave & Telecommunication Technology, 2019, vol. 30, pp. 7—11.

22. Lagovsky B. A., Samokhin A. B., Shestopalov Y. V. Angular Superresolution Based on A Priori Information. Radio Science, vol. 56, no. 1, 2021, pp. 1—11.

23. P. Charbonnier L., Blanc-F´eraud G., M. Barlaud.Deterministic edge-preserving regularization in computed imaging, IEEE Trans. Image Processing, 1997, vol. 6, no. 2, pp. 298—310.

24. Zhang Yo., Zhang Yi., Huang Y. Angular superresolution for scanning radar with improved regularized iterative adaptive approach, IEEE Geoscience and Remote Sensing Letters, 2016, vol. 13(6), pp. 1—5.

25. Nickel U. Angular superresolution with phased array radar: a review of algorithms and operational constraints, IEE Proceedings F Communications, Radar and Signal Processing, 1989, vol. 134,no. 1, pp. 53—59.

26. Yang J., Kang Y., Zhang Y.A Bayesian angular superresolution method with lognormal constraint for sea-surface target,IEEE Access, vol. 8, pp. 13419—13428.

27. Evdokimov N. A, Lukyanenko D. V., Yagola A. G. Application of multiprocessor systems for the solution of Fredholm integral equations, Comput. Methods and Programming, 2009,vol. 10, pp. 263—267.