Low bit-depth (LBD) images produce stubborn false contour artifacts and make detailed information disappear, making bit-depth enhancement (BDE) a challenging task. Considering the mixture of structural distortions and real edges in LBD images, multi-scale features are crucial for the BDE tasks. However, existing CNN-based methods suffer from structural bottlenecks, which make it difficult to capture sufficient LBD features in a single-stage network. To overcome this issue, this paper proposes a two-stage residual projection network (TRPN) to explore the multi-scale features of BDE. An encoder-decoder structure based on alternating up and down sampling is proposed to learn wide context information in stage 1. In stage 2, a residual projection module based on dense connection is proposed to preserve the detailed texture as much as possible and avoid over-smoothing in non-flat regions, which is caused by alternating up and down sampling. To efficiently utilize multi-scale features, we introduce a supervised attention module that improves network ability by dynamically adjusting the attention weights within the model. Finally, extensive experiments demonstrate that our method achieves outstanding performance improvements both quantitatively and qualitatively, which illustrates its effectiveness.