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Estimating parameters and properties of various materials without causing damage to the material under test (MUT) is important in many applications. Thus, in this letter, we address this by wireless sensing. Here, the accuracy of the estimation depends on the accurate estimation of the properties of the reflected signal from the MUT (e.g., number of reflections, their amplitudes and time delays). For a layered MUT, there are multiple reflections and, due to the limited bandwidth at the receiver, these reflections superimpose each other. Since the number of reflections coming from the MUT is limited, we propose sparse signal processing (SSP) to decompose the reflected signal. In SSP, a so called dictionary is required to obtain a sparse representation of the signal. Here, instead of a fixed dictionary, a dictionary update technique is proposed to improve the estimation of the reflected signal. To validate the proposed method, a vector network analyzer (VNA) based measurement setup is used. It turns out that the estimated dielectric constants are in close agreement with the dielectric constants of the MUTs reported in literature. Further, the proposed approach outperforms the state-of-the-art model-based curve-fitting approach in thickness estimation.