Minimum-Entropy-Based Autofocus Algorithm for SAR Data Using Chebyshev Approximation and Method of Series Reversion, and Its Implementation in a Data Processor

A novel autofocus method for synthetic aperture radar (SAR) image is studied. Based on a quadratic model for the phase error within each sub-area (narrow strip × sub-aperture) after a wide range swath is subdivided into narrow range strips and long azimuth aperture into sub-apertures, an objective function for estimation of the error is derived through the principle of minimum entropy. There is only one unknown variable in the function. With the Chebyshev approximation, the function is approximated as a polynomial, and the unknown is then solved using the method of series reversion. Curve-fitting methods are applied to estimate phase error for an entire scene of the full-swath by full-aperture. Through simulations, the proposed method is applied to restore the defocused SAR imagery that is well focused. The restored and original images are almost identical qualitatively and quantitatively. Next, the method is implemented into an existing SAR data processor. Two sets of SAR raw data at X- and Ku-bands are processed and two images are formed. Well-focused and high-resolution images from plain and rugged terrain are obtained even without the use of ancillary attitude data of the airborne SAR platform. Thus, the studied method is verified.