SAR Image Autofocus By Sharpness Optimization: A Theoretical Study

Abstract

Synthetic aperture radar (SAR) autofocus techniques that optimize sharpness metrics can produce excellent restorations in comparison with conventional autofocus approaches. To help formalize the understanding of metric-based SAR autofocus methods, and to gain more insight into their performance, we present a theoretical analysis of these techniques using simple image models. Specifically, we consider the intensity-squared metric, and a dominant point-targets image model, and derive expressions for the resulting objective function. We examine the conditions under which the perfectly focused image models correspond to stationary points of the objective function. A key contribution is that we demonstrate formally, for the specific case of intensity-squared minimization autofocus, the mechanism by which metric-based methods utilize the multichannel defocusing model of SAR autofocus to enforce the stationary point property for multiple image columns. Furthermore, our analysis shows that the objective function has a special separble property through which it can be well approximated locally by a sum of 1-D functions of each phase error component. This allows fast performance through solving a sequence of 1-D optimization problems for each phase component simultaneously. Simulation results using the proposed models and actual SAR imagery confirm that the analysis extends well to realistic situations.

On the focusing of thermal images

“…Nayar and Nakagawa, 1994;Crete et al, 2007;Gamadia, 2006;Lee et al, 2001;Zhang, 2006;Morrison et al, 2007;Wee and Paramesran, 2007;Huang and Jing, 2007;Krotov, 1987;Subbarao and Tyan, 1998), we are not aware of previous similar studies on thermal imagery.…”

Autofocusing Techniques for GPR Data from RC Bridge Decks

“…This shares certain similarity with SAR autofocusing problems. After a broad review and careful study of the successful autofocusing techniques, the potential candidates for our application are summarized into the following groups: sharpness [35], support [14], intensity [34], entropy [36], [37], contrast [33], [38], and higher-order statistics [39]. The metrics based on sharpness and minimum support will not be further discussed as they are technically semiautomatic and still involve human decision of the segmented geometrical region around the targeted object and the threshold value.…”

Model‐based adaptive synthetic aperture radar image formation algorithm

“…Because each parameter vector θ p corresponds to a range migration curve (RMC), the parameter estimation can be considered a procedure for estimating the RMC, the signal along which matches the model best [by maximising (6)]. For a deterministic t c , parameter vector θ p can be refined as θ p = [T, a 1 , a 2 ,…].…”

“…Phase gradient autofocus, the first successful autofocus algorithm widely used in practice, takes advantage of the redundancy of phase-error information by averaging many range bins [1,4]. Sharpness-maximising autofocus algorithms, another class of methods, compensate the phase errors by maximising the sharpness of the reconstructed image [5][6][7]. SAR imaging algorithms and autofocus are indispensable for generating SAR images with high quality.…”