SAR Classic WK Imaging Algorithm: Implementation and Analysis

Analysis of the Classic WK Imaging Algorithm for SAR The Omega-K algorithm (also known as WK algorithm) is an efficient frequency-domain method for Synthetic Aperture Radar (SAR) imaging. Its core principle involves implementing Range Cell Migration Correction (RCMC) through two-dimensional interpolation in the wavenumber domain (K-domain), thereby avoiding the computational complexity of traditional time-domain algorithms. When implemented on the MATLAB platform, this algorithm typically includes the following key steps: Range Direction Processing First, perform a range-direction Fast Fourier Transform (FFT) on the original echo signal to convert it to the range-frequency domain. In MATLAB, this is implemented using fft() function with proper zero-padding for spectral accuracy. At this stage, the range cell migration trajectory in the signal exhibits linear characteristics in the frequency domain, laying the foundation for subsequent correction. Wavenumber Domain Mapping Through Stolt interpolation (or Chirp-Z transform), the signal is mapped from the range-azimuth frequency domain to a unified wavenumber domain (K-domain). In MATLAB implementation, this step typically uses interp1() or interp2() functions with cubic or spline interpolation methods. This nonlinear coordinate transformation straightens the curved range migration trajectory, achieving unified processing of migration correction and focusing. Azimuth Compression After completing phase compensation in the wavenumber domain, the signal is transformed back to the image domain through Inverse Fast Fourier Transform (IFFT) using ifft() function in MATLAB, resulting in the final focused SAR image. Since the wavenumber domain directly relates to physical spatial wavelengths, this step simultaneously resolves coupling issues in both azimuth and range directions. Algorithm Advantages Avoids cumbersome point-by-point RCMC calculations Achieves precise migration correction through frequency-domain interpolation Particularly suitable for large squint or wide-beam scenarios In MATLAB implementation, special attention must be paid to interpolation accuracy and edge effect handling. Typically, sinc interpolation or nearest-neighbor interpolation is used to balance performance and efficiency. The algorithm has now become one of the standard methods for high-resolution airborne/spaceborne SAR imaging. Key MATLAB functions involved include fft, ifft, interp1, interp2, and proper windowing functions for spectral leakage control.