This paper aims to investigate the iterative reconstruction problem of low-dose computed tomography (LDCT) by adapted weighted total variation (AwTV) regularization. The motivation is based on the observation that statistical iterative reconstruction (SIR) has shown improvement of image quality in reconstruction from low-mA cone-beam CT (CBCT). More specifically, the iterative algorithm of projection onto convex set with total variation regularization (TV-POCS) has demonstrated the gains in image reconstruction from sparse angle projection data for LDCT imaging. Two approaches related to the sparse concept for LDCT imaging were investigated, one is AwTV constrained penalized weighted least-squares (AwTV-PWLS) and the other is AwTV-POCS. These two approaches were compared by experimental data from CatPhan® 600 phantom and anthropomorphic head phantom at the following conditions: (1) low-mA full view projection data, (2) normal-mA sparse view projection data, and (3) low-mA sparse view projection data. The comparison was based on the visualization evaluation and the quantitative measurements using the contrast-to-noise ratios (CNRs) merit and full-width at half-maximum measurement (FWHM) on selected regions-of-interest (ROIs) from the reconstructed images. The results indicated that the AwTV-PWLS approach can outperform the AwTV-POCS for condition (1) at 10mA level, while the AwTV-POCS algorithm has advantages for condition (2) at 80 mA level. Under the condition (3) at 10 mA level, both approaches could not yield satisfactory images. These results concur with the expectation from the theoretical models of these two approaches. The AwTV-PWLS emphasizes the data fidelity term with weighted TV penalty and is more robust for data noise while the AwTV-POCS emphasizes the sparsity nature and requires good data constraints. While the AwTV-POCS seems to serve the purpose of weighted TV minimization, a remaining open question for AwTV-PWLS is whether the weighted TV penalty is an optimal choice for the PWLS minimization. Further evaluation is needed to answer this open question.