From Matched Spatial Filtering towards the Fused Statistical Descriptive Regularization Method for Enhanced Radar Imagin
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From Matched Spatial Filtering towards the Fused Statistical Descriptive Regularization Method for Enhanced Radar Imaging Yuriy Shkvarko Cinvestav Unidad Guadalajara, Apartado Postal 31-438, Guadalajara, Jalisco 45090, Mexico Received 20 June 2005; Revised 4 November 2005; Accepted 23 November 2005 Recommended for Publication by Douglas Williams We address a new approach to solve the ill-posed nonlinear inverse problem of high-resolution numerical reconstruction of the spatial spectrum pattern (SSP) of the backscattered wavefield sources distributed over the remotely sensed scene. An array or synthesized array radar (SAR) that employs digital data signal processing is considered. By exploiting the idea of combining the statistical minimum risk estimation paradigm with numerical descriptive regularization techniques, we address a new fused statistical descriptive regularization (SDR) strategy for enhanced radar imaging. Pursuing such an approach, we establish a family of the SDR-related SSP estimators, that encompass a manifold of existing beamforming techniques ranging from traditional matched filter to robust and adaptive spatial filtering, and minimum variance methods. Copyright © 2006 Hindawi Publishing Corporation. All rights reserved.
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INTRODUCTION
In this paper, we address a new approach to enhanced array radar or SAR imaging stated and treated as an ill-posed nonlinear inverse problem. The problem at hand is to perform high-resolution reconstruction of the power spatial spectrum pattern (SSP) of the wavefield sources scattered from the probing surface (referred to as a desired image). The reconstruction is to be performed via space-time processing of finite dimensional recordings of the remotely sensed data signals distorted in a stochastic measurement channel. The SSP is defined as a spatial distribution of the power (i.e., the second-order statistics) of the random wavefield backscattered from the remotely sensed scene observed through the integral transform operator [1, 2]. Such operator is explicitly specified by the employed radar signal modulation and is traditionally referred to as the signal formation operator (SFO) [2, 3]. Moreover, in all practical remote sensing scenarios, the backscattered signals are contaminated with noise, that is, randomly distorted. Next, all digital signal recording schemes employ data sampling and quantization operations [2, 4], that is, projection of the continuous-form observations onto the finite dimensional data approximation subspaces; thus an inevitable loss of information is induced when performing such practical array data recordings. That is why the problem at hand has to be qualified and treated
as a statistical ill-conditioned nonlinear inverse problem. Because of the stochastic nature and nonlinearity, no unique analytical method exists for reconstructing the SSP from the finite dimensional measurement data in an analytic closed form, that is, via designing some nonlinear solution operator that produces the unique continuous estimate of the desired SSP [4].
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