We　propose　a　constrained　linear　data-feature-mapping　model　as　an　interpretable　mathematical　model　for　image　classification　using　a　convolutional　neural　network　(CNN).　From　this　viewpoint,　we　establish　detailed　connections　between　the　traditional　iterative　schemes　for　linear　systems　and　the　architectures　of　the　basic　blocks　of　ResNet-and　MgNet-type　models.　Using　these　connections,　we　present　some　modified　ResNet　models　that,　compared　with　the　original　models,　have　fewer　parameters　but　can　produce　more　accurate　results,　thereby　demonstrating　the　validity　of　this　constrained　learning　data　-feature-mapping　assumption.　Based　on　this　assumption,　we　further　propose　a　general　data-feature　iterative　scheme　to　demonstrate　the　rationality　of　MgNet.　We　also　provide　a　systematic　numerical　study　on　MgNet　to　show　its　success　and　advantages　in　image　classification　problems,　particularly　in　comparison　with　established　networks.(c)　2023　Elsevier　Ltd.　All　rights　reserved.