Random Scattering Kernel Modelling and Analysis by Compressed Sensing

The application of Compressed Sensing (CS) in the remote sensing technologies is a popular topic, if the sensing signal can be modelled as “simple”, e.g. sparse or low-rank, in particular spanning domains. It can reduce the complexity of sensing system, e.g. subsampling, and improve the sensing performance, e.g. super-resolution, as well. Nevertheless, this “simple” modelling of the sensing signal and moreover the design of the related sparse spanning domains are not trivial, which are strongly problem-dependent. This problem can be extremely severe e.g. for ground penetrating radar (GPR) application, where both radar coupling and scene / targets responses affect each other and result in unknown signal. To separate those unknown signal, an onsite calibration and scattering response tracking are necessary. Regarding CS modelling, we introduce the concept of “kernel function” for describing target / scene which are usually random. Given multiple measurements, there are well-known methods for kernel function tracking as MOD and KSVD. Nevertheless, they need information which are not necessarily available e.g. sparsity information and good initialization for optimization. To combat this problem, we introduced a gradually iteratively estimation of the coherent scattering kernels of data. Practical test data shows that our proposed method can provide a stable results in spite of these missing information.