PACE: an autofocus algorithm for SAR

A highly accurate phase error estimation algorithm can enable or enhance the performance of many existing and emerging applications of synthetic aperture radar (SAR). In some cases, reduction of phase error improves image exploitation. For other applications, the phase error estimate itself is of intrinsic value in extracting the desired information from SAR data. Phase Adjustment by Contrast Enhancement (PACE) is an autofocus algorithm that is capable of performance unattainable by conventional techniques. It is a nonparametric method that requires no constraints on the type of phase error to be measured. The algorithm can achieve accuracies not possible with other methods. Furthermore, it is computationally efficient, producing a given level of accuracy in less time than standard algorithms. PACE is robust in the presence of noise, and has been demonstrated to be virtually independent of scene content. The algorithm does not require special data culling techniques or the presence of isolated scatterers. PACE was originally developed for strip-mapping SAR 1 . In this paper, we discuss a slight modification of the algorithm, for the case of spotlight mode SAR. Other than the form of the focusing kernel, the two methods are identical. PACE is designed to correct a SAR image by maximizing contrast, which is defined as the ratio of the standard deviation of pixel magnitudes to the mean of pixel magnitudes. The algorithm treats the phase correction for each pulse in the azimuth dispersed data as an independent variable, with the assumption that the phase error is identical for all range bins. This choice of an object function and variables defines an unconstrained optimization problem. These types of problems can be effectively solved using an iterative, gradient-based optimization algorithm such as conjugate gradients or a quasiNewton method, provided that the gradient can be explicitly calculated. A formula has been derived for this gradient, and its calculation is straightforward and tractable, requiring about the same amount of computation as the compression of the dispersed data. The majority of the calculations performed by PACE are FFTs on independent vectors of data. Thus, like most autofocus algorithms, PACE has the important property that it can take advantage of common and well-understood hardware and software for parallel FFTs. The remaining calculations required by the algorithm also lend themselves to parallel implementation. A special version of PACE, in which the phase error is constrained to be quadratic, is also discussed. Again, this algorithm can measure phase errors with unmatched precision. Moreover, comparing this method to standard algorithms which exploit the fact that the phase error is quadratic to gain efficiency, we find that PACE outperforms other techniques in terms of time required to obtain a given level of accuracy. Section 2 defines the autofocus problem and the contrast metric used by PACE. In Section 3, we discuss the details of using an optimization algorithm to maximize the contrast function. We present results of experiments using real SAR data in Section 4, and Section 5 offers conclusions.