Quantitative imaging analysis has become a focus of medical imaging fields in recent days. In this study, Fourier-based imaging metrics for task-based quantitative assessment of lung nodules were applied in low-dose chest tomosynthesis. Compared to the conventional filtered back-projection (FBP), a compressed-sensing (CS) image reconstruction has been proposed for dose and artifact reduction. We implemented the CS-based low-dose reconstruction scheme to a sparsely sampled projection dataset and compared the lung nodule detectability index (d') between the FBP and CS methods. We used the non-prewhitening (NPW) model observer to estimate the in-plane slice detectability in tomosynthesis and theoretically calculated d' using the weighted amounts of local noise, spatial resolution, and task function in Fourier domain. We considered spatially varying noise and spatial resolution properties because the iterative reconstruction showed non-stationary characteristics. For analysis of task function, we adopted a simple binary hypothesis-testing model which discriminates outer and inner region of the encapsulated shape of lung nodule. The results indicated that the local noise power spectrum showed smaller intensities with increasing the number of projections, whereas the local transfer function provided similar appearances between the FBP and CS schemes. The resulted task functions for the same size of lung nodules showed the same pattern with different intensity, whereas the task function for different size of lung nodules presented different shapes due to different object functions. The theoretically calculated d' values showed that the CS schemes provided higher values than the FBP method by factors of 2.64-3.47 and 2.50-3.10 for two different lung nodules among all projection views. This could demonstrate that the low-dose CS algorithm provide a comparable lung nodule images in comparison to FBP from 37.9% up to 28.8% reduced dose in the same projection views. Moreover, we observed that the CS method implemented with small number of projections provided similar or somewhat higher d' values compared to the FBP method with large number of projections. In conclusion, the CS scheme may present a potential dose reduction for lung nodule detection in the chest tomosynthesis by showing higher d' in comparison to the conventional FBP method.