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The aim of this work is to develop some algebraic reconstruction techniques for low resolution power SAR imagery, as in the Scansar or QUICKLOOK imaging modes. The traditional reconstruction algorithms are indeed not well fit to low resolution power purposes, since Fourier constraints impose a computational load of the same order as the one of the usual SAR azimuthal resolution. Furthermore, the range migration balancing is superfluous, as it does not cover a tenth of the resolution cell in the less favorable situations. There are several possibilities for using matrices in the azimuthal direction. The most direct alternative leads to a matrix inversion. Unfortunately, the numerical conditioning of the problem is far from being excellent, since each line of the matrix is an image of the antenna radiating pattern with a shift between two successive lines corresponding to the distance covered by the SAR between two pulses transmission (a few meters for satellite ERS1). We'll show how it is possible to turn a very ill conditioned problem into an equivalent one, but without any divergence risk, by a technique of successive decimation by two (resolution power increased by two at each step). This technique leads to very small square matrices (two lines and two columns), the good numeric conditioning of which is certified by a well-known theorem of numerical analysis. The convergence rate of the process depends on the circumstances (mainly the distance between two impulses transmissions) and on the required accuracy, but five or six iterations already give excellent results. The process is applicable at four or five levels (number of decimations) which corresponds to initial matrices of 16 by 16 or 32 by 32. The azimuth processing is performed on the basis of the projection function concept (tomographic analogy of radar principles). This integrated information results from classical coherent range compression. The aperture synthesis is obtained by non-coherent processing of the projection functions following the above outline. A set of simulation examples are depicted, which take into account the synthetic aperture level (defined as the ratio between the antenna footprint on the ground and the required resolution in azimuth), the burst length, the number of bursts, the pulse repetition frequency, the gap between bursts, the azimuthal relative speed and other design parameters such as the number of bits for raw data or the antenna angular opening at reconstruction. The degrees of freedom of the reconstruction scheme are also outlined (possibility of filter effect for a smooth appearance or, on the other hand, a speckle impression.)
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