Neural　network　(NN)　is　a　prominent　intelligent　model　to　process　information　through　the　connection　and　activation　of　multilayer　neurons.　However,　NNs　usually　encounter　with　the　incorrect　activation　of　neurons　because　of　the　excessive　coverage　for　the　boundary　of　compound　noises.　To　address　this　issue,　this　article　proposes　a　robust　reconstructed　NN　(RRNN)　with　spectral　reshaping　activation　(SRA).　Primarily,　an　SRA　is　designed　to　replace　the　original　activation　of　NN,　which　shrinks　the　spectrums　of　the　compound　noises　toward　the　cluster　center　through　spectral　subtraction.　It　enables　RRNN　to　reshape　a　concentrated　noise　space　for　easy　coverage.　Then,　a　hierarchical　gradient　descent　(HGD)　algorithm　is　developed　to　update　the　parameters　of　RRNN.　The　HGD　algorithm　establishes　a　noise-contrastive　degree　of　SRA　to　penalize　the　loss　function　of　RRNN,　which　holds　robust　performance　with　different　noises.　Furthermore,　the　theoretical　proof　of　RRNN　is　presented　to　validate　its　robustness.　Finally,　the　experimental　results　confirm　the　superior　robustness　of　RRNN　for　tackling　noisy　samples　compared　to　other　methods.　©　2013　IEEE.