This paper address the problem of super resolution imaging, using regularized amplitude estimation. Using a Bayesian problem formulation the regularization is applied through a prior distribution of the amplitudes. We investigate both a "super Gaussian" and a Student-t prior distribution. We derive maximum a posteriori (MAP) estimators for the amplitudes, based on the "Space-Alternating Generalized Expectation-Maximization" (SAGE) method, that only uses FFT:s in each iteration. The behavior of the algorithms for different choices of regularization parameters are illustrated through simple one dimensional examples, and SAR imaging is illustrated through an example using MSTAR data.
In this paper we raise some questions about the nature and consequences of the signal model underlying SAR/ISAR imaging. One here describe a target with an object function defined over space. The measurements from a sensor is described by some other function, that are related to the object function by an operator that describe the sensor. Imaging is then the inverse problem of finding an approximation to the object function, i.e. the image, given the incomplete measurements. The usual SAR/ISAR object function is a continuous distribution of isotropic point scatterers. This distribution need to be a generalized function in order to describe the observed scattering in some cases, not only for hypothetical point scatterers, but also for a simple object such as a plate. A generalized function is of course not a true function, and there is a conceptual difficulty in viewing an image as an approximation of such an object function. A common practice is to produce calibrated images in the sense that the radar cross section of an isotropic point scatter can be directly read from the level in a magnitude-squared image. We compute such calibrated images for some simple objects such as spheres, plates and dihedrals, and show that they produce levels that not easily can be interpreted. Instead, a non trivial mix of object characteristics and imaging system characteristics such as bandwidth and aperture length influence the level at a certain image point. Even the over all appearance of the image can change. More sophisticated, "super resolving", signal processing methods postulates statistical models for the targets, and we briefly review the assumptions behind some such methods. All such methods rely on the modeling of prior information about the observed objects. This is not easy to achieve using images, which have quite a varying form even for simple objects. As an alternative, if we are prepared to leave the imaging paradigm, scattering center models give a possibility to accurately model a number of scattering phenomena. A very brief review of this promising approach is given.
In this paper we address the problem of modeling the electromagnetic scattering from targets at high frequencies as scattering centers. Scattering center models are low dimensional parametric models, that are of specific interest for automatic target recognition (ATR). The main problem with scattering center parameter estimation is the aspect dependence of range and amplitude of a scattering center. We will in this paper use scattering centers whose amplitude-aspect dependence are modeled as a polynomial of some degree, and whose range-aspect dependence are modeled as a second order polynomial. The Cramer Rao bound is derived for this problem, and estimation errors for some simple cases are illustrated. An iterative estimator for the parameters of this scattering center model is also presented, and some simple examples illustrate its performance.
ATR using HRR-signatures have recently gained lot of attention. A number of classification methods have been proposed using different target descriptions. The traditionally used classifier utilizing mean square error between magnitude only range profiles and templates suffers from problems with interfering scatterers. Several attempts to improve the MSE classifier both during the template formation process and in the matching have been made. We have recently presented a method that matches complex HRR signatures to target descriptions that use scattering centers. This method handle the unknown phases of the centers and thus overcomes the problem of interference between scatterers. In this paper we compare our method with a number of other methods that uses magnitude only range profiles. Those includes Mean-templates, Eigen- templates and the Specular and Diffuse scattering models.
KEYWORDS: Scattering, Sensors, Target recognition, Electromagnetic scattering, Data modeling, Automatic target recognition, Radar, Signal to noise ratio, Thulium, Data centers
The problem of interfering scatters in high range resolution (HRR) radar data is addressed in this paper. We derive, using a scattering center representation of target, classifiers that can handle the unknown phases of the centers. We also show how to incorporate uncertainties in the magnitudes and positions of the scattering centers. The automatic target recognition (ATR) problem is discussed in a Bayesian setting, and we show how the uncertainties can be handled by such scattering center classifiers. Monte Carlo simulations are used to evaluate the performance and robustness of the classifiers for simple test cases, and data from electromagnetic prediction codes are used to illustrate the behavior on real targets.
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