# High-Resolution Through-the-Wall Radar Imaging with Exploitation of Target Structure
## 1 Introduction  
Through-the-wall radar imaging (TWRI) as an emerging technology has attracted increasing interest owing to its capability to reveal stationary or moving targets of interest behind an opaque obstacle [1; 2; 3; 4], and it has been widely used in numerous civil and military applications, such as anti-terrorist reconnaissance, mineral resource exploration, life rescue missions, and security monitoring. TWRI aims at acquiring high-resolution images free from wall clutter and multipath. A huge number of efforts have been devoted to addressing the high-resolution TWRI issue. The time-reversal MUSIC (TR-MUSIC) was studied for through wall target detection and localization, and the simultaneous localization of multiple targets behind the wall has been achieved by employing the null space of the multistatic response matrix [5], and the performance analysis of the TR-MUSIC method was also investigated and provided in [6]. On the other hand, the multipath effect in the propagation of electromagnetic waves severely reduces the accuracy of TWRI. In addition to the directly received target echoes, multiple reflections at the walls and the targets will generate interference echoes, which lead to ghosts in the imaging and make the through-wall radar unable to accurately detect the targets. Previous studies proposed various approaches to suppress the multipath effect. By analyzing the properties of ghosts, [PERSON] et al. [7] discovered the aspect dependence (AD) of multipath scattering and suppressed the multipath ghosts based on the Hidden Markov model. Inspired by the characteristics of AD, [PERSON] et al. [8] studied the distribution characteristics of the first-order ghost of MIMO radar and applied phase coherence factor to suppress the ghosts. In contrast, some recent algorithms focused on exploiting multipath to enhance the target signal. Exploiting the information from multipaths can be successfully achieved using compressive sensing (CS) which makes use of the group sparsity of the targets caused by different propagation paths [9; 10]. The group sparsity represents thatmembers of a certain subset of entries have the same support. This means the entries in each group appear as nonzero at the same time [10]. TWRI is commonly used to image indoor humans. In indoor scenes, multipath propagations are mainly caused by the reflections on the related walls except the echo directly approaching the receiver. Group sparsity is suitable for describing the scene containing the different propagation paths, which differ in scattering coefficients but not in the nonzero spatial support. In addition to the group sparsity due to multipath, another property is the extended spatial occupancy involving the spatial region where their nonzero entries are clustered. Unfortunately, it is hard to determine the exact size and shape of the target in advance [10]. A series of algorithms have been applied to address group sparsity caused by multipath propagations [11; 12; 13; 14]. However, all of the above ignored the benefits of the target structure. Both overlapping group sparse (GS) algorithm [15] and multi-task clustered Bayesian compressive sensing (BCS) algorithms [16; 17] are developed to take clustered structure into account. However, the overlapping GS algorithm is prone to produce false targets owing to inappropriate overlapping partition. Furthermore, the multi-task BCS algorithm cannot handle the unresolvable observations caused by the multipath propagation in the TWRI. Within the hierarchical framework, this paper explores a clustered BCS algorithm in the presence of multipath propagation. High-resolution imaging is achieved by leveraging the aforementioned two types of group sparsity. We employ the group sparsity where multipath scenarios have the same nonzero support but different scattering coefficients to represent the former type. Furthermore, the latter originates from the nonzero area or volume of the target.