General side-looking synthetic aperture radar (SAR) cannot obtain scattering information about the observed scenes which are constrained by lay over and shading effects. Downward-looking sparse linear array three-dimensional SAR (DLSLA 3D SAR) can be placed on small and mobile platform, allows for the acquisition of full 3D microwave images and overcomes the restrictions of shading and lay over effects in side-looking SAR. DLSLA 3D SAR can be developed for various applications, such as city planning, environmental monitoring, Digital Elevation Model (DEM) generation, disaster relief, surveillance and reconnaissance, etc. In this paper, we give the imaging geometry and dechirp echo signal model of DLSLA 3D SAR. The sparse linear array is composed of multiple transmitting and receiving array elements placed sparsely along cross-track dimension. The radar works on time-divided transmitting-receiving mode. Particularly, the platform motion impact on the echo signal during the time-divided transmitting-receiving procedure is considered. Then we analyse the wave propagation, along-track and cross-track dimensional echo signal bandwidth before and after dechrip processing. In the following we extend the projection-slice theorem which is widely used in computerized axial tomography (CAT) to DLSLA 3D SAR imaging. In consideration of the flying platform motion compensation during time-divided transmitting-receiving procedure and parallel implementation on multi-core CPU or Graphics processing units (GPU) processor, the convolution back-projection (CBP) imaging algorithm is proposed for DLSLA 3D SAR image reconstruction. At last, the focusing capabilities of our proposed imaging algorithm are investigated and verified by numerical simulations and theoretical analysis.
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