Multi-objective　sparse　reconstruction　methods　have　shown　strong　potential　in　sparse　reconstruction.　However,　most　methods　are　computationally　expensive　due　to　the　requirement　of　excessive　functional　evaluations.　Most　of　these　methods　adopt　arbitrary　regularization　values　for　iterative　thresholding-based　local　search,　which　hardly　produces　high-precision　solutions　stably.　In　this　article,　we　propose　a　multi-objective　sparse　reconstruction　scheme　with　novel　techniques　of　transfer　learning　and　localized　regularization.　Firstly,　we　design　a　knowledge　transfer　operator　to　reuse　the　search　experience　from　previously　solved　homogeneous　or　heterogeneous　sparse　reconstruction　problems,　which　can　significantly　accelerate　the　convergence　and　improve　the　reconstruction　quality.　Secondly,　we　develop　a　localized　regularization　strategy　for　iterative　thresholding-based　local　search,　which　uses　systematically　designed　independent　regularization　values　according　to　decomposed　subproblems.　The　strategy　can　lead　to　improved　reconstruction　accuracy.　Therefore,　our　proposed　scheme　is　more　computationally　efficient　and　accurate,　compared　to　existing　multi-objective　sparse　reconstruction　methods.　This　is　validated　by　extensive　experiments　on　simulated　signals　and　benchmark　problems.