Abstract: With the widespread application of near-field millimeter-wave radar imaging technology in counter-terrorism security inspection and nondestructive testing, the Back Projection Algorithm (BPA) has been widely adopted in near-field synthetic aperture radar (SAR) imaging due to its accurate imaging model and strong adaptability to complex geometries. However, in practical applications, conventional BPA is prone to sidelobes, artifacts, and clutter noise, and it exhibits a strong dependence on the amount of echo data, which significantly degrades its imaging performance under undersampled conditions. To address these issues, an improved BPA imaging algorithm that jointly integrates image-domain structural constraints and data-domain low-rank reconstruction is proposed. In the image domain, a regularization model based on low-rank joint sparsity constraints is introduced to perform structure-preserving optimization on the initial BPA image, effectively suppressing sidelobes, artifacts, and noise interference. In the data domain, by exploiting the low-rank property of the echo data, a robust adaptive rank-one reconstruction method based on explicit regularization is developed to achieve physically consistent recovery of echo data under undersampled conditions. Experimental results demonstrate that, even with only 20% of the echo data, the proposed algorithm can achieve imaging quality comparable to or even superior to that of conventional BPA with full sampling, thereby validating its effectiveness and robustness for low-data-rate near-field millimeter-wave SAR imaging.