  Filtered backprojection (FBP) algorithm is a popular choice for complicated
trajectory SAR image formation processing due to its inherent nonlinear motion
compensation capability. However, how to efficiently autofocus the defocused
FBP imagery when the motion measurement is not accurate enough is still a
challenging problem. In this paper, a new interpretation of the FBP derivation
is presented from the Fourier transform point of view. Based on this new
viewpoint, the property of the residual 2-D phase error in FBP imagery is
analyzed in detail. Then, by incorporating the derived a priori knowledge on
the 2-D phase error, an accurate and efficient 2-D autofocus approach is
proposed. The new approach performs the parameter estimation in a
dimension-reduced parameter subspace by exploiting the a priori analytical
structure of the 2-D phase error, therefore possesses much higher accuracy and
efficiency than conventional blind methods. Finally, experimental results
clearly demonstrate the effectiveness and robustness of the proposed method.
