High　resolution　image　can　provide　good　performance　guarantee　for　other　image　processing　work,　so　image　super-resolution　has　always　been　a　hot　topic　of　research.　Image　super-resolution　based　on　sparse　representation　and　dictionary　learning　is　a　very　hot　technology,　these　method　usually　using　first-order　and　second-order　derivatives　to　extract　features　of　image,　but　this　extraction　method　can　not　effectively　extract　high-frequency　features　such　as　textures.　For　this　problem,　we　propose　a　new　single-image　super-resolution　algorithm　that　combines　concepts　from　image　decomposition　theory,　morphological　component　analysis,　coupled　dictionary　learning　and　wavelet-based　dictionary　construction.　The　LR　image　and　texture　image　layers　are　used　to　construct　coupled　dictionaries.　Coupled　dictionary　learning　is　used　to　realize　the　transformation　of　the　sparse　representation　coefficients　of　the　two　feature　spaces　through　the　mapping　matrix.　This　learning　scheme　relaxes　the　constraint　conditions,　enhances　the　mapping　relationship　between　the　LR　image　and　HR　texture　layers,　and　improves　the　reconstruction　quality.　A　set　of　dictionaries　are　created　in　the　wavelet　domain,　where　a　pair　of　sub-band　dictionaries　is　designed　for　the　structure　and　texture　image　layers　in　each　wavelet　sub-band.　A　total　of　3　pairs　of　dictionaries　have　been　constructed　for　the　structure　and　texture　image　components.　These　dictionaries　demonstrate　the　compactness,　directionality,　and　multi-scale　nature　of　the　wavelet　transform.　Hence,　our　scheme　captures　image　high-frequency　features　more　effectively.　Experimental　comparisons　show　superior　super-resolution　results　of　the　proposed　scheme　based　on　the　peak　signal-to-noise　ratio　and　the　structural　similarity　index.　©　2020　IEEE.