In this article, a matching pursuit algorithm is developed to improve the performance of a passive multiplexing technique based on compressed sensing. This deconvolution technique is applied to RADAR imaging in the microwave range, starting from previous studies based on a compact coding device and L1-norm regularizations. This study demonstrates that in this context, the quality of the reconstructed RADAR images can be improved using an algorithm close to Hogbom's Clean, and based on a dictionary built with Tikhonov pseudo-inversions. The theoretical principle of this new algorithm is developed, followed by a parameters study. Finally, an experimental validation is presented to demonstrate the efficiency of this iterative algorithm.
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