ISAR Image Improvement Using STFT Kernel Width Optimization Based On Minimum Entropy Criterion

Document Type : Research Article


1 M. Modarres-Hashemi is with the ECE Department of Isfahan University of Technology, Isfahan, Iran (email:

2 M. Dorostgan is with the ECE Department of Isfahan University of Technology, Isfahan, Iran (

3 Corresponding Author, M. M. Naghsh is with the ECE Department of Isfahan University of Technology, Isfahan, Iran (email:


Nowadays, Radar systems have many applications and radar imaging is one of the most important of these applications. Inverse Synthetic Aperture Radar (ISAR) is used to form an image from moving targets. Conventional methods use Fourier transform to retrieve Doppler information. However, because of maneuvering of the target, the Doppler spectrum becomes time-varying and the image is blurred. Joint Time-Frequency Transforms (JTFT) like Short-Time Fourier Transform (STFT) can resolve the Doppler spectrum and reduce the image blurring. These transforms use some kernels for signal spectrum analysis. According to the uncertainty principle, the proper selection of this kernel and its parameters could affect the quality of the image. In this paper, using a conventional kernel for STFT, i.e. Gaussian kernel, we use minimum entropy criterion to optimize the kernel duration. Simulation results show that this optimization can improve the constructed image compared with the Fourier transform method.


[1]     Gonzales, R. C.; Woods, R. C.; digital image processing, 2nd Edition, Prentice Hall, 2002.
[2]     Mensa, D. L.; High resolution radar cross-section imaging, 2nd Edition, Artech house, 1991.
[3]     Wehner, D. R.; High resolution radar ,2nd Edition ,
Artech house , 1994.
[4]     Chen, V. ; Ling, H.; Time-Frequency transform for radar imaging and signal analysis, Artech house, 2002.
[5]     Son,S. J.;Thmas, G.;Flore, C. B.;Range Doppler radar imaging and motion compensation, Artech house, 2000.
[6]     Xi, L. ;Guosui, L. ; Ni, J.; “Autufocusing of image based on entropy minimization”, IEEE Transaction on Aerospace and Electronic Systems, Vol. 35,No.4 ,pp. 1240-1251, 1999.
[7]     Chen, V., Qian, S. ; “Joint time-frequncy transform for radar range dopller imaging” , IEEE Transaction on Aerospace and Electronic Systems, Vol. 34, No. 2,pp.
[8]     Chen, V. ;”Reconstruction of inverse synthetic aperture radar image using adaptive time-frequency wavelet transform”, SPIE Proc. On wavelet Applications, Vol.2494 pp. 373-386, 1995.
[9]     Kersten, P.R.; Jansen, R.W.; Luc, K.; Ainsworth, T.L.;  “Implementation of the time-frequency distribution series for SAR applications”, Proceedings of IEEE International Conference on Geosciences and Remote Sensing Symposium, pp. 3587-3590, 2006.
[10]  Zhu, Y.; Wang, H.; Xiao, S.; “Application of Adaptive Kernel Time-Frequency Distribution in ISAR”, 9th International Conference on Signal Processing, 2008.
[11]  Oppenheim, A. V.; Schafer, R. W.; Buck, J. R.; Discrete time signal processing, 2nd Edition, Prentice- Hall, 1999.
[12]  M. Dorostgan; Joint time-frequency transfoms for ISAR imaging, M.Sc Thesis (In Persian), ECE Department, Isfahan University of Technology, 2004, (in Persian)..
[13]  Ho, R. J.;  Hyo, T. K.; Kyung, T. K.; “Application of Subarray Averaging and Entropy Minimization Algorithm to Stepped-Frequency ISAR Autofocus”, IEEE Transaction on antennas and propagation, Vol. 56, No. 4, 2008.
[14]  Zhu, D.; Wang, L.; Yu, Y.; Tao, Q.; Zhu, Z.; “Robust ISAR range alignment via minimizing the entropy of the average range profile”, IEEE Geoscience and remote Sensing letter, vol. 6, no. 2, pp. 204–208, Apr. 2009.
[15]  Cao, P.; Xing, M.; Sun, G.; Li, Y.; Bao, Z.; “Minimum Entropy via Subspace for ISAR Autofocus”, IEEE geoscience and remote sensing letters, Vol. PP, pp. 1-5, 2009.
[16]  Martorella, M.; Berizzi, F.; Bruscoli, S.; “Use of Genetic Algorithms for Contrast and Entropy Optimization in ISAR Autofocusing”, EURASIP Journal on Applied Signal Processing, 2006.E. H. Miller, "A note on reflector arrays," IEEE Trans. Antennas Propagat., to be published.
[17]  M. Dorostgan, M. Modarres-Hashemi, S. Sadri; Optimizing STFT based ISAR image formation using entropy and contrast criteria, ICEE, 2005, (in Persian).
[18]  Cover, T. M. ;Thomas, J. A. ; Elements of information theory, John Wiley & sons, 1991.
[19]  Chen, V.;Miceli, W. J. ; “Simulation of Isar imaging of moving targets”, IEE proc.-Radar, sonar and navigation, Vol. 148, No.3, pp. 160-166, 2001.
[20]  Hua, Y. ; Baqai, E. ; Zhu, Y. ; “Imaging of point scatterers from step-frequency ISAR data”, IEEE Transaction on Aerospace and Electronic Systems, Vol. 29,No. 1,pp. 195-204, 1993.
[21]  Shirman, Y. D. ;Computer simulation of aerial target radar scattering, recognition, detection and tracking, Artech house, 2002.
[22]  Zwieg, G.; “Super-resolution Fourier transforms by optimisation, and ISAR imaging”, IEE Proc.-Radar ,Sonar  and navigation, Vol. 150, No. 4, 2003.
[23]  Popovic, V.; Thayaparan, T.; Stankovic, L.; “Noise analysis of the high resolution methods in ISAR”, Proceedings of the 4th International Symposium on Image and Signal Processing and Analysis, 2005.
[24]  Kovaci, M.;  Isar,  D.; Isar, A.; “Denoising SAR images”, International Symposium on Signals, Circuits and Systems, 2003.
[25]  Nuthalapati, M. R. ; “High resolution construction of ISAR images”, IEEE transaction on  aerospace and electronic, Vol. 28, No. 2, 1992.
Naghsh, M. M.; Modarres-Hashemi, M. “ISAR Image Formation Based on Minimum Entropy Criterion and Fractional Fourier Transform”, IEICE transaction on communication, Vol. E92-B, No. 8, pp. 2714-2722, 2009