In　order　to　address　the　expensive　computation　cost　of　deep　networks,　some　Single　Image　Super-Resolution　(SISR)　methods　tried　to　design　the　lightweight　networks　by　means　of　recursion　or　expert　prior.　However,　they　discuss　the　theoretical　interpretation　for　the　network＇s　design　less.　To　address　this　issue,　we　propose　a　novel　method　for　constructing　an　interpretable　lightweight　deep　network　for　SISR　by　fusing　the　idea　of　model-driven　and　data-driven.　That　is,　we　give　a　theoretical　interpretation　for　the　lightweight　network＇s　design　from　the　optimization　model　of　image　degeneration.　Considering　that　ℓp(0＜p＜1)-norm　is　sparser　than　the　ℓ1-norm　and　can　describe　the　noises　of　image　degeneration　better,　our　proposed　SISR　method　firstly　deduces　an　iteration　algorithm　from　the　ℓp(0＜p＜1)　degeneration　model.　Then　according　to　this　theoretical　deduction,　an　effective　deep　network　is　designed.　Since　our　proposed　deep　network　is　designed　according　to　the　iteration　algorithm,　our　network　can　not　only　realize　the　lightweight　structure　because　of　the　weight　sharing　decided　by　the　iterative　principle,　but　also　show　a　theoretical　interpretation　for　designing　the　deep　network.　Extensive　experimental　results　illustrate　that　our　proposed　method　is　superior　to　some　related　popular　SISR　methods　with　the　lightweight　structure.　©　2024　Elsevier　B.V.