Detection　of　ship　wakes　in　SAR　images　is　helpful　not　only　in　estimating　the　speed　and　the　direction　of　moving　ships,　but　also　in　finding　small　ship　objects.　The　existing　ship　wake　detection　methods　for　SAR　images　can　achieve　satisfactory　results　only　for　simple　background,　but　can　hardly　work　for　complex　background.　In　this　paper,　a　novel　ship　wake　detection　method　for　complex　background　based　on　morphological　component　analysis　(MCA)　and　multi-dictionary　learning.　In　this　method,　a　SAR　image　is　decomposed　into　a　cartoon　component　containing　ship　wakes,　and　the　process　of　the　decomposition　is　supported　by　a　ship　wake　dictionary　built　analytically　and　renewed　iteratively.　At　the　same　time,　the　SAR　image　is　also　decomposed　into　a　texture　component　supported　by　a　sea-surface　texture　dictionary　learnt　off-line.　Then,　the　cartoon　component　is　enhanced　by　the　shearlet　transform　and　the　high-frequency　coeffcient　reconstruction.　At　last,　the　ship　wake　lines　are　detected　from　the　enhanced　cartoon　component　by　Radon　transform.　Experimental　results　show　that　the　performance　of　the　proposed　method　outperforms　other　state-of-the-art　methods　for　detection　of　ship　wakes　in　SAR　images　with　complex　background.　Copyright　©　2017　Acta　Automatica　Sinica.　All　rights　reserved.