This　paper　aims　at　solving　the　sparse　reconstruction　(SR)　problem　via　a　multiobjective　evolutionary　algorithm.　Existing　multiobjective　evolutionary　algorithms　for　the　SR　problem　have　high　computational　complexity,　especially　in　high-dimensional　reconstruction　scenarios.　Furthermore,　these　algorithms　focus　on　estimating　the　whole　Pareto　front　rather　than　the　knee　region,　thus　leading　to　limited　diversity　of　solutions　in　knee　region　and　waste　of　computational　effort.　To　tackle　these　issues,　this　paper　proposes　an　adaptive　decomposition-based　evolutionary　approach　(ADEA)　for　the　SR　problem.　Firstly,　we　employ　the　decomposition-based　evolutionary　paradigm　to　guarantee　a　high　computational　efficiency　and　diversity　of　solutions　in　the　whole　objective　space.　Then,　we　propose　a　two　stage　iterative　soft-thresholding　(IST)-based　local　search　operator　to　improve　the　convergence.　Finally,　we　develop　an　adaptive　decomposition　-based　environmental　selection　strategy,　by　which　the　decomposition　in　the　knee　region　can　be　adjusted　dynamically.　This　strategy　enables　to　focus　the　selection　effort　on　the　knee　region　and　achieves　low　computational　complexity.　Experimental　results　on　simulated　signals,　benchmark　signals　and　images　demonstrate　the　superiority　of　ADEA　in　terms　of　reconstruction　accuracy　and　computational　efficiency,　compared　to　five　state-of-the-art　algorithms.　(C)　2018　Elsevier　Inc.　All　rights　reserved.