In recent years, through-wall imaging (TWI) has gained much research interest because of urgent needs of civilian, security, and defense applications. TWI based on compressive sensing (CS) method can produce high resolution, assuming that the wall parameters are known in prior. However, it is difficult to know the exact wall parameters in actual scenarios. With unknown wall parameters, the dictionary matrix is not a fixed one. Therefore, CS theory cannot be directly applied in the TWI. This paper presents a parametric sparse recovery method for TWI with unknown wall parameters. The original reconstruction problem is reformulated into a joint optimization one which can be solved with an alternating minimization algorithm. Specifically, the proposed method performs the wall parameter estimation and sparse image reconstruction in an iterative procedure. With the estimated wall parameter which is or close to the true one, the high fidelity and high-resolution image is obtained. Experimental simulations show that the proposed method can obtain an autofocus image and improve the image quality.
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