Passive acoustic monitoring offers the potential to enable long-term, spatially extensive assessments of coral reefs. To explore this approach, we deployed underwater acoustic recorders at ten coral reef sites around Singapore waters over two years. To mitigate the persistent anthropogenic and current-induced noise masking the low-frequency reef soundscape, we trained a convolutional neural network denoiser. Analysis of the acoustic data reveals distinct morning and evening choruses. Though the correlation with environmental variates was obscured in the low-frequency part of the noisy recordings, the denoised data showed correlations of acoustic activity indices such as sound pressure level and acoustic complexity index with diver-based assessments of reef health such as live coral richness and cover, and algal cover. Furthermore, the shrimp snap rate, computed from the high-frequency acoustic band, is robustly correlated with the reef parameters, both temporally and spatially. This study demonstrates that passive acoustics holds valuable information that can help with reef monitoring, provided the data is effectively denoised and interpreted. This methodology can be extended to other marine environments where acoustic monitoring is hindered by persistent noise.