Lognormal Random-Field Models and Their Applications to Radar Image Synthesis

Lognormal random fields with multiplicative spatial interaction are proposed for modeling radar image intensity. Two particular classes of two-dimensional (2-D) lognormal random fields are introduced: multiplicative autoregressive (MAR), and multiplicative Mnrkov random fields (MMRF). The MAR and MMRF models are formulated as invertible point-transformations of Gaussian autoregressive and Gaussian Markov random fields (GMRF) and therefore possess many desirable properties. Least squares and maximum likelihood estimates for random-field parameters are presented, a decision rule is developed for selecting model order and transformations to normality as well, and techniques for synthesizing 2-D lognormal random fields are provided. Several Seasat synthetic aperture radar (SAR) images were tested using the decision rule developed in this paper and using the Kolmogorov-Smirnov (K-S) goodness-of-fit test. With both tests they were found to possess a good fit to lognormal statistics. MAR and MMRF models were fit to Seasat SAR images, and then the models were used to generate synthetic images that closely resemble the original SAR images both visually and in their variograms. This demonstrates the generality and appropriateness of the MAR and MMRF models for radar imagery.

[1]  R. Chellappa,et al.  Digital image restoration using spatial interaction models , 1982 .

[2]  G. B. Goldstein,et al.  False-Alarm Regulation in Log-Normal and Weibull Clutter , 1973, IEEE Transactions on Aerospace and Electronic Systems.

[3]  M. Ekstrom,et al.  Multidimensional spectral factorization and unilateral autoregressive models , 1980 .

[4]  Peyton Z. Peebles.  The Generation of Correlated Log-Normal Clutter for Radar Simulations , 1971, IEEE Transactions on Aerospace and Electronic Systems.

[5]  Marc S. Weiss.  Modification of the Kolmogorov-Smirnov Statistic for Use with Correlated Data , 1978 .

[6]  Hassan Mostafavi,et al.  Image Correlation with Geometric Distortion Part II: Effect on Local Accuracy , 1978, IEEE Transactions on Aerospace and Electronic Systems.

[7]  R. Kashyap.  A Bayesian comparison of different classes of dynamic models using empirical data , 1977 .

[8]  H. Künsch.  Approximations to the Maximum Likelihood Equations for Some Gaussian Random Fields , 1983 .

[9]  Rangasami L. Kashyap,et al.  Synthesis and Estimation of Random Fields Using Long-Correlation Models , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[10]  Rama Chellappa,et al.  Estimation and choice of neighbors in spatial-interaction models of images , 1983, IEEE Trans. Inf. Theory.

[11]  Fawwaz T. Ulaby,et al.  Vegetation clutter model , 1980 .

[12]  Julian Holtzman,et al.  Radar Image Simulation , 1978, IEEE Transactions on Geoscience Electronics.

[13]  K. S. Shanmugan,et al.  Crop Classification Using Airborne Radar and Landsat Data , 1982, IEEE Transactions on Geoscience and Remote Sensing.

[14]  E. Jakeman,et al.  A model for non-Rayleigh sea echo , 1976 .

[15]  J. Besag.  Spatial Interaction and the Statistical Analysis of Lattice Systems , 1974 .

[16]  J. Woods,et al.  Estimation and identification of two dimensional images , 1981, 1981 20th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes.

[17]  David J. Sakrison,et al.  The effects of a visual fidelity criterion of the encoding of images , 1974, IEEE Trans. Inf. Theory.

[18]  D. Sakrison,et al.  On the Role of the Observer and a Distortion Measure in Image Transmission , 1977, IEEE Trans. Commun..

[19]  Matsuo Sekine,et al.  Suppression of ground and weather clutter , 1981 .

[20]  R. H. Mitchel,et al.  Synthetic Aperture Radar (SAR) Image Quality Considerations , 1982 .

[21]  Rama Chellappa,et al.  A model-based approach for estimation of two-dimensional maximum entropy power spectra , 1985, IEEE Trans. Inf. Theory.

[22]  D. Lewinski.  Nonstationary probabilistic target and clutter scattering models , 1983 .

[23]  Jr. Thomas G. Stockham,et al.  Image processing in the context of a visual model , 1972 .

[24]  M. Blanco.  On Clutter Modeling and the Spectra of Two-Dimensional Gauss-Markov Random Signals , 1982, IEEE Transactions on Aerospace and Electronic Systems.

[25]  N. Abramson,et al.  Bandwidth and Spectra of Phase-and-Frequency-Modulated Waves , 1963 .