We developed a foundation for assessing visual quality with “corrupted reference” (CR-QA)—a new quality assessment (QA) paradigm for reasoning about human vision and image restoration problems jointly. In most image restoration problems, the notion of an ideal reference that exist only in theory and not in practice. CR-QA assesses the visual quality of a restored image signal relative to this ideal reference image (not provided) with the help of observed image (i.e. corrupted reference). This is in contrast to today’s QAs, which either require direct access to the ideal reference image (full-reference QA) or disregards the ideal reference entirely (no-reference QA).