Autofocus algorithms with phase error correction for synthetic aperture radar imagery

Due to the unknown platform motion and/or signal propagation delays, phase errors are introduced to synthetic aperture radar (SAR) imagery. With the fact that the pixel values in the low-return region of the focused image are close to zero, we devise two autofocus SAR imaging methods with phase error correction in this paper. One is a fractional model to maximize the pixel values in the remaining region, termed high-return region, while minimizing those in the low-return region. And another is a model with the high-return region pixel value maximization and the controlled peak low-return pixel value. The resultant optimization problems are difficult to solve due to the coupled numerator and denominator of the quadratic fractional programming problem formulation with the constant modulus constraints and the controlled optimization problem with the nonconvex inequality constraints. To tackle them, we derive two iterative solutions via introducing auxiliary variables to decouple the numerator and denominator and the inequality constraints. Alternating direction method of multipliers is utilized in the algorithm development so that their convergence is guaranteed. Numerical examples are provided to show the effectiveness of the developed methods.