The　free-energy　principle　in　recent　studies　of　brain　theory　and　neuroscience　models　the　perception　and　understanding　of　the　outside　scene　as　an　active　inference　process,　in　which　the　brain　tries　to　account　for　the　visual　scene　with　an　internal　generative　model.　Specifically,　with　the　internal　generative　model,　the　brain　yields　corresponding　predictions　for　its　encountered　visual　scenes.　Then,　the　discrepancy　between　the　visual　input　and　its　brain　prediction　should　be　closely　related　to　the　quality　of　perceptions.　On　the　other　hand,　sparse　representation　has　been　evidenced　to　resemble　the　strategy　of　the　primary　visual　cortex　in　the　brain　for　representing　natural　images.　With　the　strong　neurobiological　support　for　sparse　representation,　in　this　paper,　we　approximate　the　internal　generative　model　with　sparse　representation　and　propose　an　image　quality　metric　accordingly,　which　is　named　FSI　(free-energy　principle　and　sparse　representation-based　index　for　image　quality　assessment).　In　FSI,　the　reference　and　distorted　images　are,　respectively,　predicted　by　the　sparse　representation　at　first.　Then,　the　difference　between　the　entropies　of　the　prediction　discrepancies　is　defined　to　measure　the　image　quality.　Experimental　results　on　four　large-scale　image　databases　confirm　the　effectiveness　of　the　FSI　and　its　superiority　over　representative　image　quality　assessment　methods.　The　FSI　belongs　to　reduced-reference　methods,　and　it　only　needs　a　single　number　from　the　reference　image　for　quality　estimation.