A Novel Non-Linear Approximation to the Huygens-Fresnel Diffraction Patterns for Reconstructing Digital Holographic SAR Images

Based on the nonlinear approximation of Huygens-Fresnel diffraction patterns, the SAR images of a target can be made up from a knowledge of a hologram for all frequencies and all aspects angles to provide a complete description of the target. In this paper we reconstruct the image of hologram employing the multiresolution Fresnelet transform to approximate the Huygens-Fresnel diffraction patterns in an off-axis geometry from the simulated test pattern (3bar). Fresnel transform is a wavelet-like transform, very close to Gabor functions (M. Unser et al., 1992) and well localized with respect to the holographic process. This method allows us to generate and reconstruct hologram on a digital computer, and apply multiresolution wavelet base analysis and special filtering on it. Since images are nonstationary process, we use fractional Brownian motion (fBm) method to describe texture in SAR images. It is known as a suitable model to classify a vast number of natural phenomena and shapes, such as the range of rivers, terrain surfaces, mountains ripples of water, coastlines and etc. The novelty of this technique lies in the use of Fresnel transform in reconstruction of holographic SAR images and fBm model for classifying them