Non-line-of-sight (NLOS) imaging allows for the imaging of objects around a corner, which enables potential applications in various fields, such as autonomous driving, robotic vision, medical imaging, security monitoring, etc. However, the quality of reconstruction is challenged by low signal-to-noise ratio (SNR) measurements. In this study, we present a regularization method, referred to as structure sparsity (SS) regularization, for denoising in NLOS reconstruction. By exploiting the prior knowledge of structure sparseness, we incorporate nuclear norm penalization into the cost function of the directional light-cone transform (DLCT) model for the NLOS imaging system. This incorporation effectively integrates the neighborhood information associated with the directional albedo, thereby facilitating the denoising process. Subsequently, the reconstruction is achieved by optimizing a directional albedo model with SS regularization using the fast iterative shrinkage-thresholding algorithm (FISTA). Notably, the robust reconstruction of occluded objects is observed. Through comprehensive evaluations conducted on both synthetic and experimental datasets, we demonstrate that the proposed approach yields high-quality reconstructions, surpassing the state-of-the-art reconstruction algorithms, especially in scenarios involving short exposure and low-SNR measurements.