Multiobjective　sparse　reconstruction　(MOSR)　methods　can　potentially　obtain　superior　reconstruction　performance.　However,　they　suffer　from　high　computational　cost,　especially　in　high-dimensional　reconstruction.　Furthermore,　they　are　generally　implemented　independently　without　reusing　prior　knowledge　from　past　experiences,　leading　to　unnecessary　computational　consumption　due　to　the　re-exploration　of　similar　search　spaces.　To　address　these　problems,　we　propose　a　sparse-constraint　knowledge　transfer　operator　to　accelerate　the　convergence　of　MOSR　solvers　by　reusing　the　knowledge　from　past　problem-solving　experiences.　Firstly,　we　introduce　the　deep　nonlinear　feature　coding　method　to　extract　the　feature　mapping　between　the　search　of　the　current　problem　and　a　previously　solved　MOSR　problem.　Through　this　mapping,　we　learn　a　set　of　knowledge-induced　solutions　which　contain　the　search　experience　of　the　past　problem.　Thereafter,　we　develop　and　apply　a　sparse-constraint　strategy　to　refine　these　learned　solutions　to　guarantee　their　sparse　characteristics.　Finally,　we　inject　the　refined　solutions　into　the　iteration　of　the　current　problem　to　facilitate　the　convergence.　To　validate　the　efficiency　of　the　proposed　operator,　comprehensive　studies　on　extensive　simulated　signal　reconstruction　are　conducted.　©　Springer　Nature　Switzerland　AG　2019.