SAR back-projection focusing algorithm with a sub-apertures technique

Synthetic aperture radar (SAR) is a general method for generating high-resolution radar maps from low-resolution aperture data which is based on using the relative motion between the radar antenna and the image scene. A synthetic aperture is formed using electromagnetic signals from a physical aperture located at different space-time position. SAR can be seen as a particular case of side-looking radar in which the angular resolution is inversely proportional to the aperture size so that the spatial resolution degrades increasing the distance from the scene. Synthetic aperture is obtained combining the data from the real antenna of a side-looking real-aperture radar as we sample data of a bigger real antenna with size equal to the real-antenna footprint . In this way SAR can observe the scene over a large angular sector by moving the physical aperture to achieve a better resolution in the along-track direction with results that are independent from the range to the scene. The resolution of these system are limited by antenna illumination and system bandwidth but also by other factors, e.g. accuracy of the antenna positioning, propagation perturbation, transmitted power, etc. The ultimate limit of SAR spatial resolution is proportional to the wavelength. Signal processing play a key role in SAR because it is necessary to process all the reiceved echo for all the positions of the synethic aperture in order to obtain the final image and this is why there are many different algorithms of focusing. There are two foundamental features in the focusing algorithms: resolution and computational efficiency. Most of computationally efficient algorithms work in the Frequency-domain such as the Rectangular format algorithm or thet Fourier-Hankel and range migration inversion method. A major shortcoming of the algorithms, however, is that they are derived for a linear aperture and they are not easily extendible to the common nonlinear case. It is possible to partly correct for nonlinear motion, i.e. deviation from a linear track, but the image must be cut into subimages and processed separately since the motion correction is only locally valid. This problem becomes a major issue in wide-beam system e.g. low-frequency SAR where a wide beam is necessary to obtain an acceptable along-track resolution. There is cleary need for other processing algorithms which can be more easily adapted to a general aperture geometry, and this leads to the image formation in the time-domain. A way to consider such an algorithm is the back-projection integral used in tomography. In the direct back-projection method, each received radar echo is processed and back-projected over spherical shells to all imaged ground pixels. Each pixel is thus assigned a value by interpolating the pulse echo at the time delay corresponding to the range beetwen the pixel and the antenna. The value for each pixel is accumulated as more radar echoes are processed and the final resolution achieved. The main drawback of the direct back-projection algorithm is the large number of required operation, since every aperture position must be examined for every image pixel. The purpose of this thesys is to implement a direct back-projection integral partitioning the integral in sub-integrals each correspoding a sub-aperture. We divided the syntethic aperture in sub-apertures and then we undersample each of them to increse the algorithm's performance in term of computational cost.