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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.

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We present a new noniterative approach to synthetic aperture radar (SAR) autofocus, termed the multichannel autofocus (MCA) algorithm. The key in the approach is to exploit the multichannel redundancy of the defocusing operation to create a linear subspace, where the unknown perfectly focused image resides, expressed in terms of a known basis formed from the given defocused image. A unique solution for the perfectly focused image is then directly determined through a linear algebraic formulation by invoking an additional image support condition. The MCA approach is found to be computationally efficient and robust and does not require prior assumptions about the SAR scene used in existing methods. In addition, the vector-space formulation of MCA allows sharpness metric optimization to be easily incorporated within the restoration framework as a regularization term. We present experimental results characterizing the performance of MCA in comparison with conventional autofocus methods and discuss the practical implementation of the technique.