Adaptive Sparse Decomposition For Layered Media Parameters Inversion Of Ground Penetrating Radar Returns

There is no existing rigorous theory for dielectric properties inversion of ground penetrating radar(GPR) returns in layered media electromagnetic wave propagation models. Hence, researchers analyze radar signals relying on simplified formula or artificial debugging parameters based on experience. Furthermore, most of the current researches on parameters inversion in layered systems can only be applied to detect the single layer structure. When applied to multi-layered media, the parameters inversion precise may not be high enough. So, how to carry out efficient and accurate inversion result has been a hot issue in GPR detection area.This paper proposes to apply adaptive sparse decomposition to signal amplitude and time delay estimation and then evaluate dielectric constant and thickness by electromagnetic wave propagation model. This paper puts forward three techniques for sparse decomposition, including sparse decomposition based on Gabor dictionary, K-SVD method and four kinds of adaptive sparse decomposition algorithms (including OMP, ROMP, CoSaMP, SAMP). The simulation result verifies that the sparse decomposition based on Gabor dictionary wastes much time, the reconstruction precise isn't high enough yet. K-SVD algorithm gets rather high precision, however, it takes more time than the adaptive sparse decomposition algorithms.Three methods including deconvolution, layer stripping based on energy ratio, and sparse decomposition are proposed in this paper to evaluate signal amplitude and time delay. The deconvolution technique estimates signal reflection coefficient with the inverse of the time delay matching dictionary times the received signal vector. The time delay information can be chosen from the atoms of the dictionary where the amplitudes of the corresponding positions are nonzero. This method receives high evaluation precision but consumes a lot of time. The ratio between the energy of the received signal and a reference signal plus the time delay extracted from the received signal are the unknown elements we need to estimate signal amplitude by layer stripping based on energy ratio. This method takes the least time, however, it doesn't work when the received signal overlaps. The adaptive sparse decomposition selects time delay from the atoms in the iteration procedure, and then estimates the reflection coefficient vector. It achieves better balance between execution time and estimation accuracy, and can be applied to signal with low signal-noise-ratio. After the time delay and the reflection coefficient are estimated, the thickness and the permittivity can be evaluated layer by layer. The simulation result proves that the adaptive sparse decomposition gets the best performance for taking less time and achieving better evaluation accuracy.