# American Institute of Mathematical Sciences

May  2016, 10(2): 549-561. doi: 10.3934/ipi.2016011

## The relationship between backprojection and best linear unbiased estimation in synthetic-aperture radar imaging

 1 Colorado State University, Department of Mathematics, 1874 Campus Delivery, Fort Collins, CO 80523-1874, United States

Received  June 2015 Revised  October 2015 Published  May 2016

In this paper we investigate the relationship between two different techniques typically used in imaging and estimation problems. We focus on synthetic-aperture radar imaging and compare the methods of backprojection (standard for imaging) and best linear unbiased estimation (BLUE). We aim to reconstruct or estimate the reflectivity function of an object present in a scene of interest. We find that the estimate of the reflectivity (calculated using BLUE) and the reconstructed image (calculated using filtered backprojection) are the same when we utilize a criterion from microlocal analysis to define the optimal backprojection filter and assume the measured data is corrupted by zero-mean independently identically distributed (white) noise. In particular we show that the microlocal criterion for the optimal backprojection filter is equivalent to the unbiased constraint present in the BLUE technique.
Citation: Kaitlyn Muller. The relationship between backprojection and best linear unbiased estimation in synthetic-aperture radar imaging. Inverse Problems & Imaging, 2016, 10 (2) : 549-561. doi: 10.3934/ipi.2016011
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