There other methods to assess the quality of the reconstructed lossy compressed audio or video signal. It is the subjective tests by the so called mean opinion score. Where the subjective quality has five grades from 1 to 5 with the highest quality is assigned grade 5 and the lowest is assigned grade 1.
Conference Paper Subjective quality assessment of numerically reconstructed c...
You may want to take a look at VMAF and FRQM from Netflix.
VMAF ( Video Multi-Method Assessment Fusion ):
https://github.com/Netflix/vmaf
Li, Z., A. Norkin, and A. Aaron. "VMAF-video quality metric alternative to PSNR." Joint Video Exploration Team (JVET) of ITU-T SG 16 WP 3 and ISO/IEC JTC 1/SC 29/WG 11 (2016).