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PolSAR image classification has attracted extensive significant research in recent decades. Aiming at improving PolSAR classification performance with speckle noise, this paper proposes an active complex-valued convolutional-wavelet neural network by incorporating dual-tree complex wavelet transform (DT-CWT) and Markov random field (MRF). In this approach, DT-CWT is introduced into the complex-valued convolutional neural network to suppress the speckle noise of PolSAR images and maintain the structures of learned feature maps. In addition, by applying active learning (AL), we iteratively select the most informative unlabeled training samples of PolSAR datasets. Moreover, MRF is utilized to obtain spatial local correlation information, which has been proven to be effective in improving classification performance. The experimental results on three benchmark PolSAR datasets demonstrate that the proposed method can achieve a significant classification performance gain in terms of its effectiveness and robustness beyond some state-of-the-art deep learning methods. [ABSTRACT FROM AUTHOR]